diff --git a/synapse/crypto/context_factory.py b/synapse/crypto/context_factory.py
index cff3ca809aba..0397f73ab4f0 100644
--- a/synapse/crypto/context_factory.py
+++ b/synapse/crypto/context_factory.py
@@ -13,8 +13,8 @@
 # limitations under the License.
 
 from twisted.internet import ssl
-from OpenSSL import SSL
-from twisted.internet._sslverify import _OpenSSLECCurve, _defaultCurveName
+from OpenSSL import SSL, crypto
+from twisted.internet._sslverify import _defaultCurveName
 
 import logging
 
@@ -32,8 +32,9 @@ def __init__(self, config):
     @staticmethod
     def configure_context(context, config):
         try:
-            _ecCurve = _OpenSSLECCurve(_defaultCurveName)
-            _ecCurve.addECKeyToContext(context)
+            _ecCurve = crypto.get_elliptic_curve(_defaultCurveName)
+            context.set_tmp_ecdh(_ecCurve)
+
         except Exception:
             logger.exception("Failed to enable elliptic curve for TLS")
         context.set_options(SSL.OP_NO_SSLv2 | SSL.OP_NO_SSLv3)
diff --git a/synapse/python_dependencies.py b/synapse/python_dependencies.py
index 711cbb6c50aa..216db4d164c9 100644
--- a/synapse/python_dependencies.py
+++ b/synapse/python_dependencies.py
@@ -39,12 +39,11 @@
     "signedjson>=1.0.0": ["signedjson>=1.0.0"],
     "pynacl>=1.2.1": ["nacl>=1.2.1", "nacl.bindings"],
     "service_identity>=1.0.0": ["service_identity>=1.0.0"],
+    "Twisted>=16.0.0": ["twisted>=16.0.0"],
 
-    # we break under Twisted 18.4
-    # (https://github.com/matrix-org/synapse/issues/3135)
-    "Twisted>=16.0.0,<18.4": ["twisted>=16.0.0"],
+    # We use crypto.get_elliptic_curve which is only supported in >=0.15
+    "pyopenssl>=0.15": ["OpenSSL>=0.15"],
 
-    "pyopenssl>=0.14": ["OpenSSL>=0.14"],
     "pyyaml": ["yaml"],
     "pyasn1": ["pyasn1"],
     "daemonize": ["daemonize"],