diff --git a/tests/test_ssl.py b/tests/test_ssl.py
index e0a720b..14b2310 100644
--- a/tests/test_ssl.py
+++ b/tests/test_ssl.py
@@ -229,33 +229,13 @@
     BIOs.
     """
     def _loopbackClientFactory(self, socket):
-        client = Connection(Context(TLSv1_METHOD), socket)
-        client.set_connect_state()
-        return client
+        return loopback_client_factory(socket)
 
     def _loopbackServerFactory(self, socket):
-        ctx = Context(TLSv1_METHOD)
-        ctx.use_privatekey(load_privatekey(FILETYPE_PEM, server_key_pem))
-        ctx.use_certificate(load_certificate(FILETYPE_PEM, server_cert_pem))
-        server = Connection(ctx, socket)
-        server.set_accept_state()
-        return server
+        return loopback_server_factory(socket)
 
     def _loopback(self, serverFactory=None, clientFactory=None):
-        if serverFactory is None:
-            serverFactory = self._loopbackServerFactory
-        if clientFactory is None:
-            clientFactory = self._loopbackClientFactory
-
-        (server, client) = socket_pair()
-        server = serverFactory(server)
-        client = clientFactory(client)
-
-        handshake(client, server)
-
-        server.setblocking(True)
-        client.setblocking(True)
-        return server, client
+        return loopback(serverFactory, clientFactory)
 
     def _interactInMemory(self, client_conn, server_conn):
         return interact_in_memory(client_conn, server_conn)
@@ -264,6 +244,42 @@
         return handshake_in_memory(client_conn, server_conn)
 
 
+def loopback_client_factory(socket):
+    client = Connection(Context(TLSv1_METHOD), socket)
+    client.set_connect_state()
+    return client
+
+
+def loopback_server_factory(socket):
+    ctx = Context(TLSv1_METHOD)
+    ctx.use_privatekey(load_privatekey(FILETYPE_PEM, server_key_pem))
+    ctx.use_certificate(load_certificate(FILETYPE_PEM, server_cert_pem))
+    server = Connection(ctx, socket)
+    server.set_accept_state()
+    return server
+
+
+def loopback(server_factory=None, client_factory=None):
+    """
+    Create a connected socket pair and force two connected SSL sockets
+    to talk to each other via memory BIOs.
+    """
+    if server_factory is None:
+        server_factory = loopback_server_factory
+    if client_factory is None:
+        client_factory = loopback_client_factory
+
+    (server, client) = socket_pair()
+    server = server_factory(server)
+    client = client_factory(client)
+
+    handshake(client, server)
+
+    server.setblocking(True)
+    client.setblocking(True)
+    return server, client
+
+
 def interact_in_memory(client_conn, server_conn):
     """
     Try to read application bytes from each of the two `Connection` objects.
@@ -1956,9 +1972,9 @@
         assert isinstance(new_session, Session)
 
 
-class ConnectionTests(TestCase, _LoopbackMixin):
+class TestConnection(object):
     """
-    Unit tests for :class:`OpenSSL.SSL.Connection`.
+    Unit tests for `OpenSSL.SSL.Connection`.
     """
     # XXX get_peer_certificate -> None
     # XXX sock_shutdown
@@ -1976,57 +1992,47 @@
 
     def test_type(self):
         """
-        :py:obj:`Connection` and :py:obj:`ConnectionType` refer to the same
-        type object and can be used to create instances of that type.
+        `Connection` and `ConnectionType` refer to the same type object and
+        can be used to create instances of that type.
         """
-        self.assertIdentical(Connection, ConnectionType)
+        assert Connection is ConnectionType
         ctx = Context(TLSv1_METHOD)
-        self.assertConsistentType(Connection, 'Connection', ctx, None)
+        assert is_consistent_type(Connection, 'Connection', ctx, None)
 
     def test_get_context(self):
         """
-        :py:obj:`Connection.get_context` returns the :py:obj:`Context` instance
-        used to construct the :py:obj:`Connection` instance.
+        `Connection.get_context` returns the `Context` instance used to
+        construct the `Connection` instance.
         """
         context = Context(TLSv1_METHOD)
         connection = Connection(context, None)
-        self.assertIdentical(connection.get_context(), context)
-
-    def test_get_context_wrong_args(self):
-        """
-        :py:obj:`Connection.get_context` raises :py:obj:`TypeError` if called
-        with any arguments.
-        """
-        connection = Connection(Context(TLSv1_METHOD), None)
-        self.assertRaises(TypeError, connection.get_context, None)
+        assert connection.get_context() is context
 
     def test_set_context_wrong_args(self):
         """
-        :py:obj:`Connection.set_context` raises :py:obj:`TypeError` if called
-        with a non-:py:obj:`Context` instance argument or with any number of
-        arguments other than 1.
+        `Connection.set_context` raises `TypeError` if called with a
+        non-`Context` instance argument,
         """
         ctx = Context(TLSv1_METHOD)
         connection = Connection(ctx, None)
-        self.assertRaises(TypeError, connection.set_context)
-        self.assertRaises(TypeError, connection.set_context, object())
-        self.assertRaises(TypeError, connection.set_context, "hello")
-        self.assertRaises(TypeError, connection.set_context, 1)
-        self.assertRaises(TypeError, connection.set_context, 1, 2)
-        self.assertRaises(
-            TypeError, connection.set_context, Context(TLSv1_METHOD), 2)
-        self.assertIdentical(ctx, connection.get_context())
+        with pytest.raises(TypeError):
+            connection.set_context(object())
+        with pytest.raises(TypeError):
+            connection.set_context("hello")
+        with pytest.raises(TypeError):
+            connection.set_context(1)
+        assert ctx is connection.get_context()
 
     def test_set_context(self):
         """
-        :py:obj:`Connection.set_context` specifies a new :py:obj:`Context`
-        instance to be used for the connection.
+        `Connection.set_context` specifies a new `Context` instance to be
+        used for the connection.
         """
         original = Context(SSLv23_METHOD)
         replacement = Context(TLSv1_METHOD)
         connection = Connection(original, None)
         connection.set_context(replacement)
-        self.assertIdentical(replacement, connection.get_context())
+        assert replacement is connection.get_context()
         # Lose our references to the contexts, just in case the Connection
         # isn't properly managing its own contributions to their reference
         # counts.
@@ -2035,88 +2041,52 @@
 
     def test_set_tlsext_host_name_wrong_args(self):
         """
-        If :py:obj:`Connection.set_tlsext_host_name` is called with a non-byte
-        string argument or a byte string with an embedded NUL or other than one
-        argument, :py:obj:`TypeError` is raised.
+        If `Connection.set_tlsext_host_name` is called with a non-byte string
+        argument or a byte string with an embedded NUL, `TypeError` is raised.
         """
         conn = Connection(Context(TLSv1_METHOD), None)
-        self.assertRaises(TypeError, conn.set_tlsext_host_name)
-        self.assertRaises(TypeError, conn.set_tlsext_host_name, object())
-        self.assertRaises(TypeError, conn.set_tlsext_host_name, 123, 456)
-        self.assertRaises(
-            TypeError, conn.set_tlsext_host_name, b"with\0null")
+        with pytest.raises(TypeError):
+            conn.set_tlsext_host_name(object())
+        with pytest.raises(TypeError):
+            conn.set_tlsext_host_name(b"with\0null")
 
         if PY3:
             # On Python 3.x, don't accidentally implicitly convert from text.
-            self.assertRaises(
-                TypeError,
-                conn.set_tlsext_host_name, b"example.com".decode("ascii"))
-
-    def test_get_servername_wrong_args(self):
-        """
-        :py:obj:`Connection.get_servername` raises :py:obj:`TypeError` if
-        called with any arguments.
-        """
-        connection = Connection(Context(TLSv1_METHOD), None)
-        self.assertRaises(TypeError, connection.get_servername, object())
-        self.assertRaises(TypeError, connection.get_servername, 1)
-        self.assertRaises(TypeError, connection.get_servername, "hello")
+            with pytest.raises(TypeError):
+                conn.set_tlsext_host_name(b"example.com".decode("ascii"))
 
     def test_pending(self):
         """
-        :py:obj:`Connection.pending` returns the number of bytes available for
+        `Connection.pending` returns the number of bytes available for
         immediate read.
         """
         connection = Connection(Context(TLSv1_METHOD), None)
-        self.assertEquals(connection.pending(), 0)
-
-    def test_pending_wrong_args(self):
-        """
-        :py:obj:`Connection.pending` raises :py:obj:`TypeError` if called with
-        any arguments.
-        """
-        connection = Connection(Context(TLSv1_METHOD), None)
-        self.assertRaises(TypeError, connection.pending, None)
+        assert connection.pending() == 0
 
     def test_peek(self):
         """
-        :py:obj:`Connection.recv` peeks into the connection if
-        :py:obj:`socket.MSG_PEEK` is passed.
+        `Connection.recv` peeks into the connection if `socket.MSG_PEEK`
+        is passed.
         """
-        server, client = self._loopback()
+        server, client = loopback()
         server.send(b'xy')
-        self.assertEqual(client.recv(2, MSG_PEEK), b'xy')
-        self.assertEqual(client.recv(2, MSG_PEEK), b'xy')
-        self.assertEqual(client.recv(2), b'xy')
+        assert client.recv(2, MSG_PEEK) == b'xy'
+        assert client.recv(2, MSG_PEEK) == b'xy'
+        assert client.recv(2) == b'xy'
 
     def test_connect_wrong_args(self):
         """
-        :py:obj:`Connection.connect` raises :py:obj:`TypeError` if called with
-        a non-address argument or with the wrong number of arguments.
+        `Connection.connect` raises `TypeError` if called with
+        a non-address argument.
         """
         connection = Connection(Context(TLSv1_METHOD), socket())
-        self.assertRaises(TypeError, connection.connect, None)
-        self.assertRaises(TypeError, connection.connect)
-        self.assertRaises(
-            TypeError, connection.connect, ("127.0.0.1", 1), None
-        )
-
-    def test_connection_undefined_attr(self):
-        """
-        :py:obj:`Connection.connect` raises :py:obj:`TypeError` if called with
-        a non-address argument or with the wrong number of arguments.
-        """
-
-        def attr_access_test(connection):
-            return connection.an_attribute_which_is_not_defined
-
-        connection = Connection(Context(TLSv1_METHOD), None)
-        self.assertRaises(AttributeError, attr_access_test, connection)
+        with pytest.raises(TypeError):
+            connection.connect(None)
 
     def test_connect_refused(self):
         """
-        :py:obj:`Connection.connect` raises :py:obj:`socket.error` if the
-        underlying socket connect method raises it.
+        `Connection.connect` raises `socket.error` if the underlying socket
+        connect method raises it.
         """
         client = socket()
         context = Context(TLSv1_METHOD)
@@ -2131,8 +2101,7 @@
 
     def test_connect(self):
         """
-        :py:obj:`Connection.connect` establishes a connection to the specified
-        address.
+        `Connection.connect` establishes a connection to the specified address.
         """
         port = socket()
         port.bind(('', 0))
@@ -2148,8 +2117,8 @@
     )
     def test_connect_ex(self):
         """
-        If there is a connection error, :py:obj:`Connection.connect_ex`
-        returns the errno instead of raising an exception.
+        If there is a connection error, `Connection.connect_ex` returns the
+        errno instead of raising an exception.
         """
         port = socket()
         port.bind(('', 0))
@@ -2159,22 +2128,13 @@
         clientSSL.setblocking(False)
         result = clientSSL.connect_ex(port.getsockname())
         expected = (EINPROGRESS, EWOULDBLOCK)
-        self.assertTrue(
-            result in expected, "%r not in %r" % (result, expected))
-
-    def test_accept_wrong_args(self):
-        """
-        :py:obj:`Connection.accept` raises :py:obj:`TypeError` if called with
-        any arguments.
-        """
-        connection = Connection(Context(TLSv1_METHOD), socket())
-        self.assertRaises(TypeError, connection.accept, None)
+        assert result in expected
 
     def test_accept(self):
         """
-        :py:obj:`Connection.accept` accepts a pending connection attempt and
-        returns a tuple of a new :py:obj:`Connection` (the accepted client) and
-        the address the connection originated from.
+        `Connection.accept` accepts a pending connection attempt and returns a
+        tuple of a new `Connection` (the accepted client) and the address the
+        connection originated from.
         """
         ctx = Context(TLSv1_METHOD)
         ctx.use_privatekey(load_privatekey(FILETYPE_PEM, server_key_pem))
@@ -2192,58 +2152,53 @@
 
         serverSSL, address = portSSL.accept()
 
-        self.assertTrue(isinstance(serverSSL, Connection))
-        self.assertIdentical(serverSSL.get_context(), ctx)
-        self.assertEquals(address, clientSSL.getsockname())
+        assert isinstance(serverSSL, Connection)
+        assert serverSSL.get_context() is ctx
+        assert address == clientSSL.getsockname()
 
     def test_shutdown_wrong_args(self):
         """
-        :py:obj:`Connection.shutdown` raises :py:obj:`TypeError` if called with
-        the wrong number of arguments or with arguments other than integers.
+        `Connection.set_shutdown` raises `TypeError` if called with arguments
+        other than integers.
         """
         connection = Connection(Context(TLSv1_METHOD), None)
-        self.assertRaises(TypeError, connection.shutdown, None)
-        self.assertRaises(TypeError, connection.get_shutdown, None)
-        self.assertRaises(TypeError, connection.set_shutdown)
-        self.assertRaises(TypeError, connection.set_shutdown, None)
-        self.assertRaises(TypeError, connection.set_shutdown, 0, 1)
+        with pytest.raises(TypeError):
+            connection.set_shutdown(None)
 
     def test_shutdown(self):
         """
-        :py:obj:`Connection.shutdown` performs an SSL-level connection
-        shutdown.
+        `Connection.shutdown` performs an SSL-level connection shutdown.
         """
-        server, client = self._loopback()
-        self.assertFalse(server.shutdown())
-        self.assertEquals(server.get_shutdown(), SENT_SHUTDOWN)
-        self.assertRaises(ZeroReturnError, client.recv, 1024)
-        self.assertEquals(client.get_shutdown(), RECEIVED_SHUTDOWN)
+        server, client = loopback()
+        assert not server.shutdown()
+        assert server.get_shutdown() == SENT_SHUTDOWN
+        with pytest.raises(ZeroReturnError):
+            client.recv(1024)
+        assert client.get_shutdown() == RECEIVED_SHUTDOWN
         client.shutdown()
-        self.assertEquals(
-            client.get_shutdown(), SENT_SHUTDOWN | RECEIVED_SHUTDOWN
-        )
-        self.assertRaises(ZeroReturnError, server.recv, 1024)
-        self.assertEquals(
-            server.get_shutdown(), SENT_SHUTDOWN | RECEIVED_SHUTDOWN
-        )
+        assert client.get_shutdown() == (SENT_SHUTDOWN | RECEIVED_SHUTDOWN)
+        with pytest.raises(ZeroReturnError):
+            server.recv(1024)
+        assert server.get_shutdown() == (SENT_SHUTDOWN | RECEIVED_SHUTDOWN)
 
     def test_shutdown_closed(self):
         """
-        If the underlying socket is closed, :py:obj:`Connection.shutdown`
-        propagates the write error from the low level write call.
+        If the underlying socket is closed, `Connection.shutdown` propagates
+        the write error from the low level write call.
         """
-        server, client = self._loopback()
+        server, client = loopback()
         server.sock_shutdown(2)
-        exc = self.assertRaises(SysCallError, server.shutdown)
-        if platform == "win32":
-            self.assertEqual(exc.args[0], ESHUTDOWN)
-        else:
-            self.assertEqual(exc.args[0], EPIPE)
+        with pytest.raises(SysCallError) as exc:
+            server.shutdown()
+            if platform == "win32":
+                assert exc.value.args[0] == ESHUTDOWN
+            else:
+                assert exc.value.args[0] == EPIPE
 
     def test_shutdown_truncated(self):
         """
-        If the underlying connection is truncated, :obj:`Connection.shutdown`
-        raises an :obj:`Error`.
+        If the underlying connection is truncated, `Connection.shutdown`
+        raises an `Error`.
         """
         server_ctx = Context(TLSv1_METHOD)
         client_ctx = Context(TLSv1_METHOD)
@@ -2253,39 +2208,41 @@
             load_certificate(FILETYPE_PEM, server_cert_pem))
         server = Connection(server_ctx, None)
         client = Connection(client_ctx, None)
-        self._handshakeInMemory(client, server)
-        self.assertEqual(server.shutdown(), False)
-        self.assertRaises(WantReadError, server.shutdown)
+        handshake_in_memory(client, server)
+        assert not server.shutdown()
+        with pytest.raises(WantReadError):
+            server.shutdown()
         server.bio_shutdown()
-        self.assertRaises(Error, server.shutdown)
+        with pytest.raises(Error):
+            server.shutdown()
 
     def test_set_shutdown(self):
         """
-        :py:obj:`Connection.set_shutdown` sets the state of the SSL connection
+        `Connection.set_shutdown` sets the state of the SSL connection
         shutdown process.
         """
         connection = Connection(Context(TLSv1_METHOD), socket())
         connection.set_shutdown(RECEIVED_SHUTDOWN)
-        self.assertEquals(connection.get_shutdown(), RECEIVED_SHUTDOWN)
+        assert connection.get_shutdown() == RECEIVED_SHUTDOWN
 
     @skip_if_py3
     def test_set_shutdown_long(self):
         """
-        On Python 2 :py:obj:`Connection.set_shutdown` accepts an argument
-        of type :py:obj:`long` as well as :py:obj:`int`.
+        On Python 2 `Connection.set_shutdown` accepts an argument
+        of type `long` as well as `int`.
         """
         connection = Connection(Context(TLSv1_METHOD), socket())
         connection.set_shutdown(long(RECEIVED_SHUTDOWN))
-        self.assertEquals(connection.get_shutdown(), RECEIVED_SHUTDOWN)
+        assert connection.get_shutdown() == RECEIVED_SHUTDOWN
 
     def test_state_string(self):
         """
-        :meth:`Connection.state_string` verbosely describes the current
-        state of the :class:`Connection`.
+        `Connection.state_string` verbosely describes the current state of
+        the `Connection`.
         """
         server, client = socket_pair()
-        server = self._loopbackServerFactory(server)
-        client = self._loopbackClientFactory(client)
+        server = loopback_server_factory(server)
+        client = loopback_client_factory(client)
 
         assert server.get_state_string() in [
             b"before/accept initialization", b"before SSL initialization"
@@ -2294,22 +2251,11 @@
             b"before/connect initialization", b"before SSL initialization"
         ]
 
-    def test_app_data_wrong_args(self):
-        """
-        :py:obj:`Connection.set_app_data` raises :py:obj:`TypeError` if called
-        with other than one argument.  :py:obj:`Connection.get_app_data` raises
-        :py:obj:`TypeError` if called with any arguments.
-        """
-        conn = Connection(Context(TLSv1_METHOD), None)
-        self.assertRaises(TypeError, conn.get_app_data, None)
-        self.assertRaises(TypeError, conn.set_app_data)
-        self.assertRaises(TypeError, conn.set_app_data, None, None)
-
     def test_app_data(self):
         """
         Any object can be set as app data by passing it to
-        :py:obj:`Connection.set_app_data` and later retrieved with
-        :py:obj:`Connection.get_app_data`.
+        `Connection.set_app_data` and later retrieved with
+        `Connection.get_app_data`.
         """
         conn = Connection(Context(TLSv1_METHOD), None)
         assert None is conn.get_app_data()
@@ -2319,26 +2265,16 @@
 
     def test_makefile(self):
         """
-        :py:obj:`Connection.makefile` is not implemented and calling that
-        method raises :py:obj:`NotImplementedError`.
+        `Connection.makefile` is not implemented and calling that
+        method raises `NotImplementedError`.
         """
         conn = Connection(Context(TLSv1_METHOD), None)
-        self.assertRaises(NotImplementedError, conn.makefile)
-
-    def test_get_peer_cert_chain_wrong_args(self):
-        """
-        :py:obj:`Connection.get_peer_cert_chain` raises :py:obj:`TypeError` if
-        called with any arguments.
-        """
-        conn = Connection(Context(TLSv1_METHOD), None)
-        self.assertRaises(TypeError, conn.get_peer_cert_chain, 1)
-        self.assertRaises(TypeError, conn.get_peer_cert_chain, "foo")
-        self.assertRaises(TypeError, conn.get_peer_cert_chain, object())
-        self.assertRaises(TypeError, conn.get_peer_cert_chain, [])
+        with pytest.raises(NotImplementedError):
+            conn.makefile()
 
     def test_get_peer_cert_chain(self):
         """
-        :py:obj:`Connection.get_peer_cert_chain` returns a list of certificates
+        `Connection.get_peer_cert_chain` returns a list of certificates
         which the connected server returned for the certification verification.
         """
         chain = _create_certificate_chain()
@@ -2358,21 +2294,18 @@
         client = Connection(clientContext, None)
         client.set_connect_state()
 
-        self._interactInMemory(client, server)
+        interact_in_memory(client, server)
 
         chain = client.get_peer_cert_chain()
-        self.assertEqual(len(chain), 3)
-        self.assertEqual(
-            "Server Certificate", chain[0].get_subject().CN)
-        self.assertEqual(
-            "Intermediate Certificate", chain[1].get_subject().CN)
-        self.assertEqual(
-            "Authority Certificate", chain[2].get_subject().CN)
+        assert len(chain) == 3
+        assert "Server Certificate" == chain[0].get_subject().CN
+        assert "Intermediate Certificate" == chain[1].get_subject().CN
+        assert "Authority Certificate" == chain[2].get_subject().CN
 
     def test_get_peer_cert_chain_none(self):
         """
-        :py:obj:`Connection.get_peer_cert_chain` returns :py:obj:`None` if the
-        peer sends no certificate chain.
+        `Connection.get_peer_cert_chain` returns `None` if the peer sends
+        no certificate chain.
         """
         ctx = Context(TLSv1_METHOD)
         ctx.use_privatekey(load_privatekey(FILETYPE_PEM, server_key_pem))
@@ -2381,71 +2314,57 @@
         server.set_accept_state()
         client = Connection(Context(TLSv1_METHOD), None)
         client.set_connect_state()
-        self._interactInMemory(client, server)
-        self.assertIdentical(None, server.get_peer_cert_chain())
-
-    def test_get_session_wrong_args(self):
-        """
-        :py:obj:`Connection.get_session` raises :py:obj:`TypeError` if called
-        with any arguments.
-        """
-        ctx = Context(TLSv1_METHOD)
-        server = Connection(ctx, None)
-        self.assertRaises(TypeError, server.get_session, 123)
-        self.assertRaises(TypeError, server.get_session, "hello")
-        self.assertRaises(TypeError, server.get_session, object())
+        interact_in_memory(client, server)
+        assert None is server.get_peer_cert_chain()
 
     def test_get_session_unconnected(self):
         """
-        :py:obj:`Connection.get_session` returns :py:obj:`None` when used with
-        an object which has not been connected.
+        `Connection.get_session` returns `None` when used with an object
+        which has not been connected.
         """
         ctx = Context(TLSv1_METHOD)
         server = Connection(ctx, None)
         session = server.get_session()
-        self.assertIdentical(None, session)
+        assert None is session
 
     def test_server_get_session(self):
         """
-        On the server side of a connection, :py:obj:`Connection.get_session`
-        returns a :py:class:`Session` instance representing the SSL session for
-        that connection.
+        On the server side of a connection, `Connection.get_session` returns a
+        `Session` instance representing the SSL session for that connection.
         """
-        server, client = self._loopback()
+        server, client = loopback()
         session = server.get_session()
-        self.assertIsInstance(session, Session)
+        assert isinstance(session, Session)
 
     def test_client_get_session(self):
         """
-        On the client side of a connection, :py:obj:`Connection.get_session`
-        returns a :py:class:`Session` instance representing the SSL session for
+        On the client side of a connection, `Connection.get_session`
+        returns a `Session` instance representing the SSL session for
         that connection.
         """
-        server, client = self._loopback()
+        server, client = loopback()
         session = client.get_session()
-        self.assertIsInstance(session, Session)
+        assert isinstance(session, Session)
 
     def test_set_session_wrong_args(self):
         """
-        If called with an object that is not an instance of
-        :py:class:`Session`, or with other than one argument,
-        :py:obj:`Connection.set_session` raises :py:obj:`TypeError`.
+        `Connection.set_session` raises `TypeError` if called with an object
+        that is not an instance of `Session`.
         """
         ctx = Context(TLSv1_METHOD)
         connection = Connection(ctx, None)
-        self.assertRaises(TypeError, connection.set_session)
-        self.assertRaises(TypeError, connection.set_session, 123)
-        self.assertRaises(TypeError, connection.set_session, "hello")
-        self.assertRaises(TypeError, connection.set_session, object())
-        self.assertRaises(
-            TypeError, connection.set_session, Session(), Session())
+        with pytest.raises(TypeError):
+            connection.set_session(123)
+        with pytest.raises(TypeError):
+            connection.set_session("hello")
+        with pytest.raises(TypeError):
+            connection.set_session(object())
 
     def test_client_set_session(self):
         """
-        :py:obj:`Connection.set_session`, when used prior to a connection being
-        established, accepts a :py:class:`Session` instance and causes an
-        attempt to re-use the session it represents when the SSL handshake is
-        performed.
+        `Connection.set_session`, when used prior to a connection being
+        established, accepts a `Session` instance and causes an attempt to
+        re-use the session it represents when the SSL handshake is performed.
         """
         key = load_privatekey(FILETYPE_PEM, server_key_pem)
         cert = load_certificate(FILETYPE_PEM, server_cert_pem)
@@ -2459,17 +2378,17 @@
             server.set_accept_state()
             return server
 
-        originalServer, originalClient = self._loopback(
-            serverFactory=makeServer)
+        originalServer, originalClient = loopback(
+            server_factory=makeServer)
         originalSession = originalClient.get_session()
 
         def makeClient(socket):
-            client = self._loopbackClientFactory(socket)
+            client = loopback_client_factory(socket)
             client.set_session(originalSession)
             return client
-        resumedServer, resumedClient = self._loopback(
-            serverFactory=makeServer,
-            clientFactory=makeClient)
+        resumedServer, resumedClient = loopback(
+            server_factory=makeServer,
+            client_factory=makeClient)
 
         # This is a proxy: in general, we have no access to any unique
         # identifier for the session (new enough versions of OpenSSL expose
@@ -2477,15 +2396,13 @@
         # Instead, exploit the fact that the master key is re-used if the
         # session is re-used.  As long as the master key for the two
         # connections is the same, the session was re-used!
-        self.assertEqual(
-            originalServer.master_key(), resumedServer.master_key())
+        assert originalServer.master_key() == resumedServer.master_key()
 
     def test_set_session_wrong_method(self):
         """
-        If :py:obj:`Connection.set_session` is passed a :py:class:`Session`
-        instance associated with a context using a different SSL method than
-        the :py:obj:`Connection` is using, a :py:class:`OpenSSL.SSL.Error` is
-        raised.
+        If `Connection.set_session` is passed a `Session` instance associated
+        with a context using a different SSL method than the `Connection`
+        is using, a `OpenSSL.SSL.Error` is raised.
         """
         # Make this work on both OpenSSL 1.0.0, which doesn't support TLSv1.2
         # and also on OpenSSL 1.1.0 which doesn't support SSLv3. (SSL_ST_INIT
@@ -2514,8 +2431,8 @@
             client.set_connect_state()
             return client
 
-        originalServer, originalClient = self._loopback(
-            serverFactory=makeServer, clientFactory=makeOriginalClient)
+        originalServer, originalClient = loopback(
+            server_factory=makeServer, client_factory=makeOriginalClient)
         originalSession = originalClient.get_session()
 
         def makeClient(socket):
@@ -2525,14 +2442,13 @@
             client.set_session(originalSession)
             return client
 
-        self.assertRaises(
-            Error,
-            self._loopback, clientFactory=makeClient, serverFactory=makeServer)
+        with pytest.raises(Error):
+            loopback(client_factory=makeClient, server_factory=makeServer)
 
     def test_wantWriteError(self):
         """
-        :py:obj:`Connection` methods which generate output raise
-        :py:obj:`OpenSSL.SSL.WantWriteError` if writing to the connection's BIO
+        `Connection` methods which generate output raise
+        `OpenSSL.SSL.WantWriteError` if writing to the connection's BIO
         fail indicating a should-write state.
         """
         client_socket, server_socket = socket_pair()
@@ -2551,57 +2467,57 @@
                     break
                 raise
         else:
-            self.fail(
+            pytest.fail(
                 "Failed to fill socket buffer, cannot test BIO want write")
 
         ctx = Context(TLSv1_METHOD)
         conn = Connection(ctx, client_socket)
         # Client's speak first, so make it an SSL client
         conn.set_connect_state()
-        self.assertRaises(WantWriteError, conn.do_handshake)
+        with pytest.raises(WantWriteError):
+            conn.do_handshake()
 
     # XXX want_read
 
     def test_get_finished_before_connect(self):
         """
-        :py:obj:`Connection.get_finished` returns :py:obj:`None` before TLS
-        handshake is completed.
+        `Connection.get_finished` returns `None` before TLS handshake
+        is completed.
         """
         ctx = Context(TLSv1_METHOD)
         connection = Connection(ctx, None)
-        self.assertEqual(connection.get_finished(), None)
+        assert connection.get_finished() is None
 
     def test_get_peer_finished_before_connect(self):
         """
-        :py:obj:`Connection.get_peer_finished` returns :py:obj:`None` before
-        TLS handshake is completed.
+        `Connection.get_peer_finished` returns `None` before TLS handshake
+        is completed.
         """
         ctx = Context(TLSv1_METHOD)
         connection = Connection(ctx, None)
-        self.assertEqual(connection.get_peer_finished(), None)
+        assert connection.get_peer_finished() is None
 
     def test_get_finished(self):
         """
-        :py:obj:`Connection.get_finished` method returns the TLS Finished
-        message send from client, or server. Finished messages are send during
+        `Connection.get_finished` method returns the TLS Finished message send
+        from client, or server. Finished messages are send during
         TLS handshake.
         """
+        server, client = loopback()
 
-        server, client = self._loopback()
-
-        self.assertNotEqual(server.get_finished(), None)
-        self.assertTrue(len(server.get_finished()) > 0)
+        assert server.get_finished() is not None
+        assert len(server.get_finished()) > 0
 
     def test_get_peer_finished(self):
         """
-        :py:obj:`Connection.get_peer_finished` method returns the TLS Finished
+        `Connection.get_peer_finished` method returns the TLS Finished
         message received from client, or server. Finished messages are send
         during TLS handshake.
         """
-        server, client = self._loopback()
+        server, client = loopback()
 
-        self.assertNotEqual(server.get_peer_finished(), None)
-        self.assertTrue(len(server.get_peer_finished()) > 0)
+        assert server.get_peer_finished() is not None
+        assert len(server.get_peer_finished()) > 0
 
     def test_tls_finished_message_symmetry(self):
         """
@@ -2611,109 +2527,148 @@
         The TLS Finished message send by client must be the TLS Finished
         message received by server.
         """
-        server, client = self._loopback()
+        server, client = loopback()
 
-        self.assertEqual(server.get_finished(), client.get_peer_finished())
-        self.assertEqual(client.get_finished(), server.get_peer_finished())
+        assert server.get_finished() == client.get_peer_finished()
+        assert client.get_finished() == server.get_peer_finished()
 
     def test_get_cipher_name_before_connect(self):
         """
-        :py:obj:`Connection.get_cipher_name` returns :py:obj:`None` if no
-        connection has been established.
+        `Connection.get_cipher_name` returns `None` if no connection
+        has been established.
         """
         ctx = Context(TLSv1_METHOD)
         conn = Connection(ctx, None)
-        self.assertIdentical(conn.get_cipher_name(), None)
+        assert conn.get_cipher_name() is None
 
     def test_get_cipher_name(self):
         """
-        :py:obj:`Connection.get_cipher_name` returns a :py:class:`unicode`
-        string giving the name of the currently used cipher.
+        `Connection.get_cipher_name` returns a `unicode` string giving the
+        name of the currently used cipher.
         """
-        server, client = self._loopback()
+        server, client = loopback()
         server_cipher_name, client_cipher_name = \
             server.get_cipher_name(), client.get_cipher_name()
 
-        self.assertIsInstance(server_cipher_name, text_type)
-        self.assertIsInstance(client_cipher_name, text_type)
+        assert isinstance(server_cipher_name, text_type)
+        assert isinstance(client_cipher_name, text_type)
 
-        self.assertEqual(server_cipher_name, client_cipher_name)
+        assert server_cipher_name == client_cipher_name
 
     def test_get_cipher_version_before_connect(self):
         """
-        :py:obj:`Connection.get_cipher_version` returns :py:obj:`None` if no
-        connection has been established.
+        `Connection.get_cipher_version` returns `None` if no connection
+        has been established.
         """
         ctx = Context(TLSv1_METHOD)
         conn = Connection(ctx, None)
-        self.assertIdentical(conn.get_cipher_version(), None)
+        assert conn.get_cipher_version() is None
 
     def test_get_cipher_version(self):
         """
-        :py:obj:`Connection.get_cipher_version` returns a :py:class:`unicode`
-        string giving the protocol name of the currently used cipher.
+        `Connection.get_cipher_version` returns a `unicode` string giving
+        the protocol name of the currently used cipher.
         """
-        server, client = self._loopback()
+        server, client = loopback()
         server_cipher_version, client_cipher_version = \
             server.get_cipher_version(), client.get_cipher_version()
 
-        self.assertIsInstance(server_cipher_version, text_type)
-        self.assertIsInstance(client_cipher_version, text_type)
+        assert isinstance(server_cipher_version, text_type)
+        assert isinstance(client_cipher_version, text_type)
 
-        self.assertEqual(server_cipher_version, client_cipher_version)
+        assert server_cipher_version == client_cipher_version
 
     def test_get_cipher_bits_before_connect(self):
         """
-        :py:obj:`Connection.get_cipher_bits` returns :py:obj:`None` if no
-        connection has been established.
+        `Connection.get_cipher_bits` returns `None` if no connection has
+        been established.
         """
         ctx = Context(TLSv1_METHOD)
         conn = Connection(ctx, None)
-        self.assertIdentical(conn.get_cipher_bits(), None)
+        assert conn.get_cipher_bits() is None
 
     def test_get_cipher_bits(self):
         """
-        :py:obj:`Connection.get_cipher_bits` returns the number of secret bits
+        `Connection.get_cipher_bits` returns the number of secret bits
         of the currently used cipher.
         """
-        server, client = self._loopback()
+        server, client = loopback()
         server_cipher_bits, client_cipher_bits = \
             server.get_cipher_bits(), client.get_cipher_bits()
 
-        self.assertIsInstance(server_cipher_bits, int)
-        self.assertIsInstance(client_cipher_bits, int)
+        assert isinstance(server_cipher_bits, int)
+        assert isinstance(client_cipher_bits, int)
 
-        self.assertEqual(server_cipher_bits, client_cipher_bits)
+        assert server_cipher_bits == client_cipher_bits
 
     def test_get_protocol_version_name(self):
         """
-        :py:obj:`Connection.get_protocol_version_name()` returns a string
-        giving the protocol version of the current connection.
+        `Connection.get_protocol_version_name()` returns a string giving the
+        protocol version of the current connection.
         """
-        server, client = self._loopback()
+        server, client = loopback()
         client_protocol_version_name = client.get_protocol_version_name()
         server_protocol_version_name = server.get_protocol_version_name()
 
-        self.assertIsInstance(server_protocol_version_name, text_type)
-        self.assertIsInstance(client_protocol_version_name, text_type)
+        assert isinstance(server_protocol_version_name, text_type)
+        assert isinstance(client_protocol_version_name, text_type)
 
-        self.assertEqual(
-            server_protocol_version_name, client_protocol_version_name
-        )
+        assert server_protocol_version_name == client_protocol_version_name
 
     def test_get_protocol_version(self):
         """
-        :py:obj:`Connection.get_protocol_version()` returns an integer
+        `Connection.get_protocol_version()` returns an integer
         giving the protocol version of the current connection.
         """
-        server, client = self._loopback()
+        server, client = loopback()
         client_protocol_version = client.get_protocol_version()
         server_protocol_version = server.get_protocol_version()
 
-        self.assertIsInstance(server_protocol_version, int)
-        self.assertIsInstance(client_protocol_version, int)
+        assert isinstance(server_protocol_version, int)
+        assert isinstance(client_protocol_version, int)
 
-        self.assertEqual(server_protocol_version, client_protocol_version)
+        assert server_protocol_version == client_protocol_version
+
+    def test_wantReadError(self):
+        """
+        `Connection.bio_read` raises `OpenSSL.SSL.WantReadError` if there are
+        no bytes available to be read from the BIO.
+        """
+        ctx = Context(TLSv1_METHOD)
+        conn = Connection(ctx, None)
+        with pytest.raises(WantReadError):
+            conn.bio_read(1024)
+
+    def test_buffer_size(self):
+        """
+        `Connection.bio_read` accepts an integer giving the maximum number
+        of bytes to read and return.
+        """
+        ctx = Context(TLSv1_METHOD)
+        conn = Connection(ctx, None)
+        conn.set_connect_state()
+        try:
+            conn.do_handshake()
+        except WantReadError:
+            pass
+        data = conn.bio_read(2)
+        assert 2 == len(data)
+
+    @skip_if_py3
+    def test_buffer_size_long(self):
+        """
+        On Python 2 `Connection.bio_read` accepts values of type `long` as
+        well as `int`.
+        """
+        ctx = Context(TLSv1_METHOD)
+        conn = Connection(ctx, None)
+        conn.set_connect_state()
+        try:
+            conn.do_handshake()
+        except WantReadError:
+            pass
+        data = conn.bio_read(long(2))
+        assert 2 == len(data)
 
 
 class ConnectionGetCipherListTests(TestCase):
@@ -3618,52 +3573,6 @@
         self._check_client_ca_list(set_replaces_add_ca)
 
 
-class TestConnection(object):
-    """
-    Tests for `Connection.bio_read` and `Connection.bio_write`.
-    """
-    def test_wantReadError(self):
-        """
-        `Connection.bio_read` raises `OpenSSL.SSL.WantReadError` if there are
-        no bytes available to be read from the BIO.
-        """
-        ctx = Context(TLSv1_METHOD)
-        conn = Connection(ctx, None)
-        with pytest.raises(WantReadError):
-            conn.bio_read(1024)
-
-    def test_buffer_size(self):
-        """
-        `Connection.bio_read` accepts an integer giving the maximum number
-        of bytes to read and return.
-        """
-        ctx = Context(TLSv1_METHOD)
-        conn = Connection(ctx, None)
-        conn.set_connect_state()
-        try:
-            conn.do_handshake()
-        except WantReadError:
-            pass
-        data = conn.bio_read(2)
-        assert 2 == len(data)
-
-    @skip_if_py3
-    def test_buffer_size_long(self):
-        """
-        On Python 2 `Connection.bio_read` accepts values of type `long` as
-        well as `int`.
-        """
-        ctx = Context(TLSv1_METHOD)
-        conn = Connection(ctx, None)
-        conn.set_connect_state()
-        try:
-            conn.do_handshake()
-        except WantReadError:
-            pass
-        data = conn.bio_read(long(2))
-        assert 2 == len(data)
-
-
 class InfoConstantTests(TestCase):
     """
     Tests for assorted constants exposed for use in info callbacks.