diff --git a/OpenSSL/test/test_crypto.py b/OpenSSL/test/test_crypto.py
index ba4e0d5..0773342 100644
--- a/OpenSSL/test/test_crypto.py
+++ b/OpenSSL/test/test_crypto.py
@@ -31,7 +31,9 @@
 from OpenSSL.crypto import NetscapeSPKI, NetscapeSPKIType
 from OpenSSL.crypto import (
     sign, verify, get_elliptic_curve, get_elliptic_curves)
-from OpenSSL.test.util import EqualityTestsMixin, TestCase
+from OpenSSL.test.util import (
+    EqualityTestsMixin, TestCase, WARNING_TYPE_EXPECTED
+)
 from OpenSSL._util import native, lib
 
 def normalize_certificate_pem(pem):
@@ -2006,14 +2008,16 @@
                               b"-passout", b"pass:" + passwd)
         with catch_warnings(record=True) as w:
             simplefilter("always")
-            if not PY3:
-                p12 = load_pkcs12(p12_str, passphrase=unicode("whatever"))
-                self.assertTrue("unicode in passphrase is no longer accepted, "
-                                "use bytes" in str(w[-1].message))
-            else:
-                p12 = load_pkcs12(p12_str, passphrase=b"whatever".decode())
-                self.assertTrue("str in passphrase is no longer accepted, "
-                                "use bytes" in str(w[-1].message))
+            p12 = load_pkcs12(p12_str, passphrase=u"whatever")
+
+            self.assertEqual(
+                u"{} for passphrase is no longer accepted, use bytes".format(
+                    WARNING_TYPE_EXPECTED
+                ),
+                str(w[-1].message)
+            )
+            self.assertIs(w[-1].category, DeprecationWarning)
+
         self.verify_pkcs12_container(p12)
 
 
@@ -2226,14 +2230,14 @@
 
         with catch_warnings(record=True) as w:
             simplefilter("always")
-            if not PY3:
-                dumped_p12 = p12.export(passphrase=unicode('randomtext'))
-                self.assertTrue("unicode in passphrase is no longer accepted, "
-                                "use bytes" in str(w[-1].message))
-            else:
-                dumped_p12 = p12.export(passphrase=b'randomtext'.decode())
-                self.assertTrue("str in passphrase is no longer accepted, "
-                                "use bytes" in str(w[-1].message))
+            dumped_p12 = p12.export(passphrase=u"randomtext")
+            self.assertEqual(
+                u"{} for passphrase is no longer accepted, use bytes".format(
+                    WARNING_TYPE_EXPECTED
+                ),
+                str(w[-1].message)
+            )
+            self.assertIs(w[-1].category, DeprecationWarning)
         self.check_recovery(
             dumped_p12, key=server_key_pem, cert=server_cert_pem, passwd=b"randomtext")
 
@@ -3201,20 +3205,13 @@
         :py:obj:`sign` generates a cryptographic signature which :py:obj:`verify` can check.
         Deprecation warnings raised because using text instead of bytes as content
         """
-        if not PY3:
-            content = unicode(
-                "It was a bright cold day in April, and the clocks were striking "
-                "thirteen. Winston Smith, his chin nuzzled into his breast in an "
-                "effort to escape the vile wind, slipped quickly through the "
-                "glass doors of Victory Mansions, though not quickly enough to "
-                "prevent a swirl of gritty dust from entering along with him.")
-        else:
-            content = b(
-                "It was a bright cold day in April, and the clocks were striking "
-                "thirteen. Winston Smith, his chin nuzzled into his breast in an "
-                "effort to escape the vile wind, slipped quickly through the "
-                "glass doors of Victory Mansions, though not quickly enough to "
-                "prevent a swirl of gritty dust from entering along with him.").decode()
+        content = (
+            u"It was a bright cold day in April, and the clocks were striking "
+            u"thirteen. Winston Smith, his chin nuzzled into his breast in an "
+            u"effort to escape the vile wind, slipped quickly through the "
+            u"glass doors of Victory Mansions, though not quickly enough to "
+            u"prevent a swirl of gritty dust from entering along with him."
+        )
 
         priv_key = load_privatekey(FILETYPE_PEM, root_key_pem)
         cert = load_certificate(FILETYPE_PEM, root_cert_pem)
@@ -3222,21 +3219,26 @@
             with catch_warnings(record=True) as w:
                 simplefilter("always")
                 sig = sign(priv_key, content, digest)
-                if not PY3:
-                    self.assertTrue("unicode in data is no longer accepted, "
-                                    "use bytes" in str(w[-1].message))
-                else:
-                    self.assertTrue("str in data is no longer accepted, "
-                                    "use bytes" in str(w[-1].message))
+
+                self.assertEqual(
+                    u"{} for data is no longer accepted, use bytes".format(
+                        WARNING_TYPE_EXPECTED
+                    ),
+                    str(w[-1].message)
+                )
+                self.assertIs(w[-1].category, DeprecationWarning)
+
             with catch_warnings(record=True) as w:
                 simplefilter("always")
                 verify(cert, sig, content, digest)
-                if not PY3:
-                    self.assertTrue("unicode in data is no longer accepted, "
-                                    "use bytes" in str(w[-1].message))
-                else:
-                    self.assertTrue("str in data is no longer accepted, "
-                                    "use bytes" in str(w[-1].message))
+
+                self.assertEqual(
+                    u"{} for data is no longer accepted, use bytes".format(
+                        WARNING_TYPE_EXPECTED
+                    ),
+                    str(w[-1].message)
+                )
+                self.assertIs(w[-1].category, DeprecationWarning)
 
 
     def test_sign_nulls(self):
diff --git a/OpenSSL/test/test_ssl.py b/OpenSSL/test/test_ssl.py
index 960c109..16bbf39 100644
--- a/OpenSSL/test/test_ssl.py
+++ b/OpenSSL/test/test_ssl.py
@@ -1,3 +1,5 @@
+
+
 # Copyright (C) Jean-Paul Calderone
 # See LICENSE for details.
 
@@ -44,7 +46,7 @@
 from OpenSSL.SSL import (
     Context, ContextType, Session, Connection, ConnectionType, SSLeay_version)
 
-from OpenSSL.test.util import TestCase, b
+from OpenSSL.test.util import WARNING_TYPE_EXPECTED, TestCase, b
 from OpenSSL.test.test_crypto import (
     cleartextCertificatePEM, cleartextPrivateKeyPEM)
 from OpenSSL.test.test_crypto import (
@@ -920,24 +922,24 @@
 
     def test_load_verify_warning(self):
         """
-        :py:obj:`Context.load_verify_locations` accepts a file name and uses the
-        certificates within for verification purposes. Raises a warning when
-        using a text in cafile.
+        :py:obj:`Context.load_verify_locations` accepts a file name and uses
+        the certificates within for verification purposes. Raises a warning
+        when using a text in cafile.
         """
-        cafile = self.mktemp()
-        fObj = open(cafile, 'w')
-        fObj.write(cleartextCertificatePEM.decode('ascii'))
-        fObj.close()
+        cafile = self.mktemp().decode("utf-8")
+        with open(cafile, 'w') as fObj:
+            fObj.write(cleartextCertificatePEM.decode("ascii"))
 
         with catch_warnings(record=True) as w:
             simplefilter("always")
-            if not PY3:
-                self._load_verify_locations_test(unicode(cafile))
-                self.assertTrue("unicode in cafile is no longer accepted, use bytes" in str(w[-1].message))
-            else:
-                self._load_verify_locations_test(cafile.decode())
-                self.assertTrue("str in cafile is no longer accepted, use bytes" in str(w[-1].message))
-            self.assertTrue(issubclass(w[-1].category, DeprecationWarning))
+            self._load_verify_locations_test(cafile)
+            self.assertEqual(
+                u"{} for cafile is no longer accepted, use bytes".format(
+                    WARNING_TYPE_EXPECTED
+                ),
+                str(w[-1].message)
+            )
+            self.assertIs(DeprecationWarning, w[-1].category)
 
 
     def test_load_verify_invalid_file(self):
@@ -2259,21 +2261,22 @@
 
     def test_text(self):
         """
-        When passed a text, :py:obj:`Connection.send` transmits all of it and returns
-        the number of bytes sent. It also raises a DeprecationWarning.
+        When passed a text, :py:obj:`Connection.send` transmits all of it and
+        returns the number of bytes sent. It also raises a DeprecationWarning.
         """
         server, client = self._loopback()
         with catch_warnings(record=True) as w:
             simplefilter("always")
-            if PY3:
-                count = server.send(b'xy'.decode())
-                self.assertTrue("str in buf is no longer accepted, use bytes" in str(w[-1].message))
-            else:
-                count = server.send(unicode('xy'))
-                self.assertTrue("unicode in buf is no longer accepted, use bytes" in str(w[-1].message))
-            self.assertTrue(issubclass(w[-1].category, DeprecationWarning))
+            count = server.send(u"xy")
+            self.assertEqual(
+                u"{} for buf is no longer accepted, use bytes".format(
+                    WARNING_TYPE_EXPECTED
+                ),
+                str(w[-1].message)
+            )
+            self.assertIs(w[-1].category, DeprecationWarning)
         self.assertEquals(count, 2)
-        self.assertEquals(client.recv(2), b('xy'))
+        self.assertEquals(client.recv(2), b"xy")
 
     try:
         memoryview
@@ -2345,14 +2348,15 @@
         server, client = self._loopback()
         with catch_warnings(record=True) as w:
             simplefilter("always")
-            if PY3:
-                server.sendall(b'x'.decode())
-                self.assertTrue("str in buf is no longer accepted, use bytes" in str(w[-1].message))
-            else:
-                server.sendall(unicode('x'))
-                self.assertTrue("unicode in buf is no longer accepted, use bytes" in str(w[-1].message))
-            self.assertTrue(issubclass(w[-1].category, DeprecationWarning))
-        self.assertEquals(client.recv(1), b('x'))
+            server.sendall(u"x")
+            self.assertEqual(
+                u"{} for buf is no longer accepted, use bytes".format(
+                    WARNING_TYPE_EXPECTED
+                ),
+                str(w[-1].message)
+            )
+            self.assertIs(w[-1].category, DeprecationWarning)
+        self.assertEquals(client.recv(1), b"x")
 
 
     try:
diff --git a/OpenSSL/test/util.py b/OpenSSL/test/util.py
index 4260eb0..b69e538 100644
--- a/OpenSSL/test/util.py
+++ b/OpenSSL/test/util.py
@@ -14,6 +14,8 @@
 from unittest import TestCase
 import sys
 
+from six import PY3
+
 from OpenSSL._util import exception_from_error_queue
 from OpenSSL.crypto import Error
 
@@ -447,3 +449,10 @@
         a = self.anInstance()
         b = Delegate()
         self.assertEqual(a != b, [b])
+
+
+# The type name expected in warnings about using the wrong string type.
+if PY3:
+    WARNING_TYPE_EXPECTED = "str"
+else:
+    WARNING_TYPE_EXPECTED = "unicode"