diff --git a/OpenSSL/SSL.py b/OpenSSL/SSL.py
index e5ae085..c5b233b 100644
--- a/OpenSSL/SSL.py
+++ b/OpenSSL/SSL.py
@@ -124,31 +124,6 @@
 SSL_CB_HANDSHAKE_START = _lib.SSL_CB_HANDSHAKE_START
 SSL_CB_HANDSHAKE_DONE = _lib.SSL_CB_HANDSHAKE_DONE
 
-def _get_elliptic_curves(lib):
-    """
-    Load the names of the supported elliptic curves from OpenSSL.
-
-    :param lib: The OpenSSL library binding object.
-    :return: A set of :py:obj:`unicode` giving the names of the elliptic curves
-        the underlying library supports.
-    """
-    if lib.Cryptography_HAS_EC:
-        num_curves = lib.EC_get_builtin_curves(_ffi.NULL, 0)
-        builtin_curves = _ffi.new('EC_builtin_curve[]', num_curves)
-        # The return value on this call should be num_curves again.  We could
-        # check it to make sure but if it *isn't* then.. what could we do?
-        # Abort the whole process, I suppose...?  -exarkun
-        lib.EC_get_builtin_curves(builtin_curves, num_curves)
-        return set(
-            _ffi.string(lib.OBJ_nid2sn(c.nid)).decode("ascii")
-            for c in builtin_curves)
-    else:
-        return set()
-
-ELLIPTIC_CURVES = _get_elliptic_curves()
-
-
-
 class Error(Exception):
     """
     An error occurred in an `OpenSSL.SSL` API.
@@ -653,48 +628,17 @@
         _lib.SSL_CTX_set_tmp_dh(self._context, dh)
 
 
-    def _set_tmp_ecdh_curve_by_nid(self, name, nid):
-        """
-        Select a curve to use by the OpenSSL NID associated with that curve.
-
-        :param name: The name of the curve identified by the NID.
-        :type name: str
-
-        :param nid: The OpenSSL NID to use.
-        :type nid: int
-
-        :raise UnsupportedEllipticCurve: If the given NID does not identify a
-            supported curve.
-        """
-        ecdh = _lib.EC_KEY_new_by_curve_name(nid)
-        if ecdh == _ffi.NULL:
-            raise UnsupportedEllipticCurve(name)
-        _lib.SSL_CTX_set_tmp_ecdh(self._context, ecdh)
-        _lib.EC_KEY_free(ecdh)
-
-
-    def set_tmp_ecdh_curve(self, curve_name):
+    def set_tmp_ecdh_curve(self, curve):
         """
         Select a curve to use for ECDHE key exchange.
 
-        The valid values of *curve_name* are the keys in
-        :py:data:OpenSSL.SSL.ELLIPTIC_CURVE_DESCRIPTIONS.
+        :param curve: A curve object to use as returned by either
+            :py:meth:`OpenSSL.crypto.get_elliptic_curve` or
+            :py:meth:`OpenSSL.crypto.get_elliptic_curves`.
 
-        Raises a subclass of ``ValueError`` if the linked OpenSSL was
-        not compiled with elliptical curve support or the specified
-        curve is not available.  You can check the specific subclass,
-        but, in general, you should just handle ``ValueError``.
-
-        :param curve_name: The 'short name' of a curve, e.g. 'prime256v1'
-        :type curve_name: str
         :return: None
         """
-        if _lib.Cryptography_HAS_EC:
-            nid = _lib.OBJ_sn2nid(curve_name.encode('ascii'))
-            if nid == _lib.NID_undef:
-                raise UnknownObject(curve_name)
-            return self._set_tmp_ecdh_curve_by_nid(curve_name, nid)
-        raise ECNotAvailable()
+        _lib.SSL_CTX_set_tmp_ecdh(self._context, curve._to_EC_KEY())
 
 
     def set_cipher_list(self, cipher_list):
diff --git a/OpenSSL/crypto.py b/OpenSSL/crypto.py
index 65e28d7..948402c 100644
--- a/OpenSSL/crypto.py
+++ b/OpenSSL/crypto.py
@@ -263,6 +263,75 @@
 
 
 
+class _EllipticCurve(object):
+    """
+    :ivar _lib: The :py:mod:`cryptography` binding instance used to interface
+        with OpenSSL.
+
+    :ivar _nid: The OpenSSL NID identifying the curve this object represents.
+    :type _nid: :py:class:`int`
+
+    :ivar name: The OpenSSL short name identifying the curve this object
+        represents.
+    :type name: :py:class:`unicode`
+    """
+    @classmethod
+    def _get_elliptic_curves(cls, lib):
+        """
+        Load the names of the supported elliptic curves from OpenSSL.
+
+        :param lib: The OpenSSL library binding object.
+        :return: A set of :py:obj:`unicode` giving the names of the elliptic curves
+            the underlying library supports.
+        """
+        if lib.Cryptography_HAS_EC:
+            num_curves = lib.EC_get_builtin_curves(_ffi.NULL, 0)
+            builtin_curves = _ffi.new('EC_builtin_curve[]', num_curves)
+            # The return value on this call should be num_curves again.  We could
+            # check it to make sure but if it *isn't* then.. what could we do?
+            # Abort the whole process, I suppose...?  -exarkun
+            lib.EC_get_builtin_curves(builtin_curves, num_curves)
+            return set(
+                cls.from_nid(lib, c.nid)
+                for c in builtin_curves)
+        else:
+            return set()
+
+
+    @classmethod
+    def from_nid(cls, lib, nid):
+        return cls(lib, nid, _ffi.string(lib.OBJ_nid2sn(nid)).decode("ascii"))
+
+
+    def __init__(self, lib, nid, name):
+        self._lib = lib
+        self._nid = nid
+        self.name = name
+
+
+    def __repr__(self):
+        return "<Curve %r>" % (self.name,)
+
+
+    def _to_EC_KEY(self):
+        key = self._lib.EC_KEY_new_by_curve_name(self._nid)
+        return _ffi.gc(key, _lib.EC_KEY_free)
+
+
+
+def get_elliptic_curves():
+    return _EllipticCurve._get_elliptic_curves(_lib)
+
+
+
+def get_elliptic_curve(name):
+    for curve in get_elliptic_curves():
+        if curve.name == name:
+            return curve
+    raise ValueError("unknown curve name", name)
+
+
+
 class X509Name(object):
     def __init__(self, name):
         """
diff --git a/OpenSSL/test/test_crypto.py b/OpenSSL/test/test_crypto.py
index a3685a9..b288985 100644
--- a/OpenSSL/test/test_crypto.py
+++ b/OpenSSL/test/test_crypto.py
@@ -25,9 +25,10 @@
 from OpenSSL.crypto import PKCS12, PKCS12Type, load_pkcs12
 from OpenSSL.crypto import CRL, Revoked, load_crl
 from OpenSSL.crypto import NetscapeSPKI, NetscapeSPKIType
-from OpenSSL.crypto import sign, verify
+from OpenSSL.crypto import (
+    sign, verify, get_elliptic_curve, get_elliptic_curves)
 from OpenSSL.test.util import TestCase, b
-from OpenSSL._util import native
+from OpenSSL._util import native, lib
 
 def normalize_certificate_pem(pem):
     return dump_certificate(FILETYPE_PEM, load_certificate(FILETYPE_PEM, pem))
@@ -3058,5 +3059,81 @@
         verify(good_cert, sig, content, "sha1")
 
 
+
+class EllipticCurveTests(TestCase):
+    """
+    Tests for :py:class:`_EllipticCurve`, :py:obj:`get_elliptic_curve`, and
+    :py:obj:`get_elliptic_curves`.
+    """
+    def test_set(self):
+        """
+        :py:obj:`get_elliptic_curves` returns a :py:obj:`set`.
+        """
+        self.assertIsInstance(get_elliptic_curves(), set)
+
+
+    def test_some_curves(self):
+        """
+        If :py:mod:`cryptography` has elliptic curve support then the set
+        returned by :py:obj:`get_elliptic_curves` has some elliptic curves in
+        it.
+
+        There could be an OpenSSL that violates this assumption.  If so, this
+        test will fail and we'll find out.
+        """
+        curves = get_elliptic_curves()
+        if lib.Cryptography_HAS_EC:
+            self.assertTrue(curves)
+        else:
+            self.assertFalse(curves)
+
+
+    def test_a_curve(self):
+        """
+        :py:obj:`get_elliptic_curve` can be used to retrieve a particular
+        supported curve.
+        """
+        curves = get_elliptic_curves()
+        if curves:
+            curve = next(iter(curves))
+            self.assertEqual(curve.name, get_elliptic_curve(curve.name).name)
+        else:
+            self.assertRaises(ValueError, get_elliptic_curve, u"prime256v1")
+
+
+    def test_not_a_curve(self):
+        """
+        :py:obj:`get_elliptic_curve` raises :py:class:`ValueError` if called
+        with a name which does not identify a supported curve.
+        """
+        self.assertRaises(
+            ValueError, get_elliptic_curve, u"this curve was just invented")
+
+
+    def test_repr(self):
+        """
+        The string representation of a curve object includes simply states the
+        object is a curve and what its name is.
+        """
+        curves = get_elliptic_curves()
+        if curves:
+            curve = next(iter(curves))
+            self.assertEqual("<Curve %r>" % (curve.name,), repr(curve))
+
+
+    def test_to_EC_KEY(self):
+        """
+        The curve object can export a version of itself as an EC_KEY* via the
+        private :py:meth:`_EllipticCurve._to_EC_KEY`.
+        """
+        curves = get_elliptic_curves()
+        if curves:
+            curve = next(iter(curves))
+            # It's not easy to assert anything about this object.  However, see
+            # leakcheck/crypto.py for a test that demonstrates it at least does
+            # not leak memory.
+            curve._to_EC_KEY()
+
+
 if __name__ == '__main__':
     main()
diff --git a/OpenSSL/test/test_ssl.py b/OpenSSL/test/test_ssl.py
index fdeff9d..6231143 100644
--- a/OpenSSL/test/test_ssl.py
+++ b/OpenSSL/test/test_ssl.py
@@ -20,6 +20,7 @@
 from OpenSSL.crypto import PKey, X509, X509Extension, X509Store
 from OpenSSL.crypto import dump_privatekey, load_privatekey
 from OpenSSL.crypto import dump_certificate, load_certificate
+from OpenSSL.crypto import get_elliptic_curves
 
 from OpenSSL.SSL import _lib
 from OpenSSL.SSL import OPENSSL_VERSION_NUMBER, SSLEAY_VERSION, SSLEAY_CFLAGS
@@ -36,9 +37,6 @@
     SESS_CACHE_OFF, SESS_CACHE_CLIENT, SESS_CACHE_SERVER, SESS_CACHE_BOTH,
     SESS_CACHE_NO_AUTO_CLEAR, SESS_CACHE_NO_INTERNAL_LOOKUP,
     SESS_CACHE_NO_INTERNAL_STORE, SESS_CACHE_NO_INTERNAL)
-from OpenSSL.SSL import (
-    _Cryptography_HAS_EC, ELLIPTIC_CURVE_DESCRIPTIONS,
-    ECNotAvailable, UnknownObject, UnsupportedEllipticCurve)
 
 from OpenSSL.SSL import (
     Error, SysCallError, WantReadError, WantWriteError, ZeroReturnError)
@@ -1179,101 +1177,13 @@
     def test_set_tmp_ecdh_curve(self):
         """
         :py:obj:`Context.set_tmp_ecdh_curve` sets the elliptic curve for
-        Diffie-Hellman to the specified named curve.
+        Diffie-Hellman to the specified curve.
         """
         context = Context(TLSv1_METHOD)
-        for curve in ELLIPTIC_CURVE_DESCRIPTIONS.keys():
-            context.set_tmp_ecdh_curve(curve)  # Must not throw.
-
-
-    def test_set_tmp_ecdh_curve_not_available(self):
-        """
-        :py:obj:`Context.set_tmp_ecdh_curve` raises :py:obj:`ECNotAvailable` if
-        elliptic curve support is not available from the underlying OpenSSL
-        version at all.
-        """
-        has_ec = _lib.Cryptography_HAS_EC
-        try:
-            _lib.Cryptography_HAS_EC = False
-
-            context = Context(TLSv1_METHOD)
-            self.assertRaises(
-                ECNotAvailable,
-                context.set_tmp_ecdh_curve, next(iter(ELLIPTIC_CURVE_DESCRIPTIONS)))
-        finally:
-            _lib.Cryptography_HAS_EC = has_ec
-
-
-    def test_set_tmp_ecdh_curve_bad_curve_name(self):
-        """
-        :py:obj:`Context.set_tmp_ecdh_curve` raises :py:obj:`UnknownObject` if
-        passed a curve_name that OpenSSL does not recognize and EC is
-        available.
-        """
-        context = Context(TLSv1_METHOD)
-        try:
-            context.set_tmp_ecdh_curve('not_an_elliptic_curve')
-        except ECNotAvailable:
-            self.assertFalse(_Cryptography_HAS_EC)
-        except UnknownObject:
-            self.assertTrue(_Cryptography_HAS_EC)
-        else:
-            self.fail(
-                "set_tmp_ecdh_curve did not fail when called with "
-                "non-existent curve name")
-
-
-    def test_set_tmp_ecdh_curve_bad_nid(self):
-        """
-        :py:obj:`Context._set_tmp_ecdh_curve_by_nid`, an implementation detail
-        of :py:obj:`Context.set_tmp_ecdh_curve`, raises
-        :py:obj:`UnsupportedEllipticCurve` raises if passed a NID that does not
-        identify a supported curve.
-        """
-        context = Context(TLSv1_METHOD)
-        try:
-            context._set_tmp_ecdh_curve_by_nid(
-                u("curve"), _lib.OBJ_sn2nid(b"sha256"))
-        except UnsupportedEllipticCurve:
-            pass
-        else:
-            self.fail(
-                "_set_tmp_ecdh_curve_by_nid did not raise "
-                "UnsupportedEllipticCurve for a NID that does not "
-                "identify a supported curve.")
-
-
-    def test_set_tmp_ecdh_curve_not_a_curve(self):
-        """
-        :py:obj:`Context.set_tmp_ecdh_curve` raises
-        :py:obj:`UnsupportedEllipticCurve` if passed a curve_name that OpenSSL
-        cannot instantiate as an elliptic curve.  It raises
-        :py:obj:`ECNotAvailable` if EC is not available at all.
-        """
-        context = Context(TLSv1_METHOD)
-        try:
-            context.set_tmp_ecdh_curve('sha256')
-        except ECNotAvailable:
-            self.assertFalse(_Cryptography_HAS_EC)
-        except UnknownObject:
-            self.assertTrue(_Cryptography_HAS_EC)
-        else:
-            self.fail(
-                "set_tmp_ecdh_curve did not fail when called with "
-                "a name that is not an elliptic curve")
-
-
-    def test_has_curve_descriptions(self):
-        """
-        If the underlying cryptography bindings claim to have elliptic
-        curve support, there should be at least one curve.
-
-        (In theory there could be an OpenSSL that violates this
-        assumption. If so, this test will fail and we'll find out.)
-
-        """
-        if _Cryptography_HAS_EC:
-            self.assertNotEqual(len(ELLIPTIC_CURVE_DESCRIPTIONS), 0)
+        for curve in get_elliptic_curves():
+            # The only easily "assertable" thing is that it does not raise an
+            # exception.
+            context.set_tmp_ecdh_curve(curve)
 
 
     def test_set_cipher_list_bytes(self):
diff --git a/doc/api/crypto.rst b/doc/api/crypto.rst
index ee93cfb..974e516 100644
--- a/doc/api/crypto.rst
+++ b/doc/api/crypto.rst
@@ -119,6 +119,28 @@
     Generic exception used in the :py:mod:`.crypto` module.
 
 
+.. py:function:: get_elliptic_curves
+
+    Return a set of objects representing the elliptic curves supported in the
+    OpenSSL build in use.
+
+    The curve objects have a :py:class:`unicode` ``name`` attribute by which
+    they identifying themselves.
+
+    The curve objects are useful as values for the argument accepted by
+    :py:meth:`Context.set_tmp_ecdh_curve` to specify which elliptical curve
+    should be used for ECDHE key exchange.
+
+
+.. py:function:: get_elliptic_curve
+
+    Return a single curve object selected by name.
+
+    See :py:func:`get_elliptic_curves` for information about curve objects.
+
+    If the named curve is not supported then :py:class:`ValueError` is raised.
+
+
 .. py:function:: dump_certificate(type, cert)
 
     Dump the certificate *cert* into a buffer string encoded with the type
diff --git a/doc/api/ssl.rst b/doc/api/ssl.rst
index b7eca70..9016e98 100644
--- a/doc/api/ssl.rst
+++ b/doc/api/ssl.rst
@@ -110,17 +110,6 @@
      .. versionadded:: 0.14
 
 
-.. py:data:: ELLIPTIC_CURVE_DESCRIPTIONS
-
-    A dictionary mapping short names of elliptic curves to textual
-    descriptions.  This dictionary contains exactly the set of curves
-    supported by the OpenSSL build in use.
-
-    The keys are the curve names that can be passed into
-    Constants used with :py:meth:`Context.set_tmp_ecdh_curve` to
-    specify which elliptical curve should be used for ECDHE key exchange.
-
-
 .. py:data:: OPENSSL_VERSION_NUMBER
 
     An integer giving the version number of the OpenSSL library used to build this
@@ -327,21 +316,15 @@
 
     Load parameters for Ephemeral Diffie-Hellman from *dhfile*.
 
-.. py:method:: Context.set_tmp_ecdh_curve(curve_name)
+
+.. py:method:: Context.set_tmp_ecdh_curve(curve)
 
    Select a curve to use for ECDHE key exchange.
 
-   The valid values of *curve_name* are the keys in
-   :py:data:`ELLIPTIC_CURVE_DESCRIPTIONS`.
+   The valid values of *curve* are the objects returned by
+   :py:func:`OpenSSL.crypto.get_elliptic_curves` or
+   :py:func:`OpenSSL.crypto.get_elliptic_curve`.
 
-   Raises a subclass of ``ValueError`` if the linked OpenSSL was not
-   compiled with elliptical curve support or the specified curve is
-   not available.  You can check the specific subclass, but, in
-   general, you should just handle ``ValueError``.
-
-   :param curve_name: The 'short name' of a curve, e.g. 'prime256v1'
-   :type curve_name: str
-   :return: None
 
 .. py:method:: Context.set_app_data(data)
 
diff --git a/leakcheck/crypto.py b/leakcheck/crypto.py
index f5fe2f8..ca79b7c 100644
--- a/leakcheck/crypto.py
+++ b/leakcheck/crypto.py
@@ -5,7 +5,7 @@
 
 from OpenSSL.crypto import (
     FILETYPE_PEM, TYPE_DSA, Error, PKey, X509, load_privatekey, CRL, Revoked,
-    _X509_REVOKED_dup)
+    get_elliptic_curves, _X509_REVOKED_dup)
 
 from OpenSSL._util import lib as _lib
 
@@ -145,6 +145,22 @@
 
 
 
+class Checker_EllipticCurve(BaseChecker):
+    """
+    Leak checks for :py:obj:`_EllipticCurve`.
+    """
+    def check_to_EC_KEY(self):
+        """
+        Repeatedly create an EC_KEY* from an :py:obj:`_EllipticCurve`.  The
+        structure should be automatically garbage collected.
+        """
+        curves = get_elliptic_curves()
+        if curves:
+            curve = next(iter(curves))
+            for i in xrange(self.iterations * 1000):
+                curve._to_EC_KEY()
+
+
 def vmsize():
     return [x for x in file('/proc/self/status').readlines() if 'VmSize' in x]