diff --git a/changelog.d/7094.misc b/changelog.d/7094.misc
new file mode 100644
index 000000000..aa093ee3c
--- /dev/null
+++ b/changelog.d/7094.misc
@@ -0,0 +1,1 @@
+Improve performance when making HTTPS requests to sygnal, sydent, etc, by sharing the SSL context object between connections.
diff --git a/synapse/crypto/context_factory.py b/synapse/crypto/context_factory.py
index e93f0b370..a5a2a7815 100644
--- a/synapse/crypto/context_factory.py
+++ b/synapse/crypto/context_factory.py
@@ -75,7 +75,7 @@ class ServerContextFactory(ContextFactory):
 
 
 @implementer(IPolicyForHTTPS)
-class ClientTLSOptionsFactory(object):
+class FederationPolicyForHTTPS(object):
     """Factory for Twisted SSLClientConnectionCreators that are used to make connections
     to remote servers for federation.
 
@@ -103,15 +103,15 @@ class ClientTLSOptionsFactory(object):
         # let us do).
         minTLS = _TLS_VERSION_MAP[config.federation_client_minimum_tls_version]
 
-        self._verify_ssl = CertificateOptions(
+        _verify_ssl = CertificateOptions(
             trustRoot=trust_root, insecurelyLowerMinimumTo=minTLS
         )
-        self._verify_ssl_context = self._verify_ssl.getContext()
-        self._verify_ssl_context.set_info_callback(self._context_info_cb)
+        self._verify_ssl_context = _verify_ssl.getContext()
+        self._verify_ssl_context.set_info_callback(_context_info_cb)
 
-        self._no_verify_ssl = CertificateOptions(insecurelyLowerMinimumTo=minTLS)
-        self._no_verify_ssl_context = self._no_verify_ssl.getContext()
-        self._no_verify_ssl_context.set_info_callback(self._context_info_cb)
+        _no_verify_ssl = CertificateOptions(insecurelyLowerMinimumTo=minTLS)
+        self._no_verify_ssl_context = _no_verify_ssl.getContext()
+        self._no_verify_ssl_context.set_info_callback(_context_info_cb)
 
     def get_options(self, host: bytes):
 
@@ -136,23 +136,6 @@ class ClientTLSOptionsFactory(object):
 
         return SSLClientConnectionCreator(host, ssl_context, should_verify)
 
-    @staticmethod
-    def _context_info_cb(ssl_connection, where, ret):
-        """The 'information callback' for our openssl context object."""
-        # we assume that the app_data on the connection object has been set to
-        # a TLSMemoryBIOProtocol object. (This is done by SSLClientConnectionCreator)
-        tls_protocol = ssl_connection.get_app_data()
-        try:
-            # ... we further assume that SSLClientConnectionCreator has set the
-            # '_synapse_tls_verifier' attribute to a ConnectionVerifier object.
-            tls_protocol._synapse_tls_verifier.verify_context_info_cb(
-                ssl_connection, where
-            )
-        except:  # noqa: E722, taken from the twisted implementation
-            logger.exception("Error during info_callback")
-            f = Failure()
-            tls_protocol.failVerification(f)
-
     def creatorForNetloc(self, hostname, port):
         """Implements the IPolicyForHTTPS interace so that this can be passed
         directly to agents.
@@ -160,6 +143,43 @@ class ClientTLSOptionsFactory(object):
         return self.get_options(hostname)
 
 
+@implementer(IPolicyForHTTPS)
+class RegularPolicyForHTTPS(object):
+    """Factory for Twisted SSLClientConnectionCreators that are used to make connections
+    to remote servers, for other than federation.
+
+    Always uses the same OpenSSL context object, which uses the default OpenSSL CA
+    trust root.
+    """
+
+    def __init__(self):
+        trust_root = platformTrust()
+        self._ssl_context = CertificateOptions(trustRoot=trust_root).getContext()
+        self._ssl_context.set_info_callback(_context_info_cb)
+
+    def creatorForNetloc(self, hostname, port):
+        return SSLClientConnectionCreator(hostname, self._ssl_context, True)
+
+
+def _context_info_cb(ssl_connection, where, ret):
+    """The 'information callback' for our openssl context objects.
+
+    Note: Once this is set as the info callback on a Context object, the Context should
+    only be used with the SSLClientConnectionCreator.
+    """
+    # we assume that the app_data on the connection object has been set to
+    # a TLSMemoryBIOProtocol object. (This is done by SSLClientConnectionCreator)
+    tls_protocol = ssl_connection.get_app_data()
+    try:
+        # ... we further assume that SSLClientConnectionCreator has set the
+        # '_synapse_tls_verifier' attribute to a ConnectionVerifier object.
+        tls_protocol._synapse_tls_verifier.verify_context_info_cb(ssl_connection, where)
+    except:  # noqa: E722, taken from the twisted implementation
+        logger.exception("Error during info_callback")
+        f = Failure()
+        tls_protocol.failVerification(f)
+
+
 @implementer(IOpenSSLClientConnectionCreator)
 class SSLClientConnectionCreator(object):
     """Creates openssl connection objects for client connections.
diff --git a/synapse/http/client.py b/synapse/http/client.py
index d4c285445..379754582 100644
--- a/synapse/http/client.py
+++ b/synapse/http/client.py
@@ -244,9 +244,6 @@ class SimpleHttpClient(object):
         pool.maxPersistentPerHost = max((100 * CACHE_SIZE_FACTOR, 5))
         pool.cachedConnectionTimeout = 2 * 60
 
-        # The default context factory in Twisted 14.0.0 (which we require) is
-        # BrowserLikePolicyForHTTPS which will do regular cert validation
-        # 'like a browser'
         self.agent = ProxyAgent(
             self.reactor,
             connectTimeout=15,
diff --git a/synapse/http/federation/matrix_federation_agent.py b/synapse/http/federation/matrix_federation_agent.py
index 647d26dc5..f5f917f5a 100644
--- a/synapse/http/federation/matrix_federation_agent.py
+++ b/synapse/http/federation/matrix_federation_agent.py
@@ -45,7 +45,7 @@ class MatrixFederationAgent(object):
     Args:
         reactor (IReactor): twisted reactor to use for underlying requests
 
-        tls_client_options_factory (ClientTLSOptionsFactory|None):
+        tls_client_options_factory (FederationPolicyForHTTPS|None):
             factory to use for fetching client tls options, or none to disable TLS.
 
         _srv_resolver (SrvResolver|None):
diff --git a/synapse/server.py b/synapse/server.py
index fd2f69e92..1b980371d 100644
--- a/synapse/server.py
+++ b/synapse/server.py
@@ -26,7 +26,6 @@ import logging
 import os
 
 from twisted.mail.smtp import sendmail
-from twisted.web.client import BrowserLikePolicyForHTTPS
 
 from synapse.api.auth import Auth
 from synapse.api.filtering import Filtering
@@ -35,6 +34,7 @@ from synapse.appservice.api import ApplicationServiceApi
 from synapse.appservice.scheduler import ApplicationServiceScheduler
 from synapse.config.homeserver import HomeServerConfig
 from synapse.crypto import context_factory
+from synapse.crypto.context_factory import RegularPolicyForHTTPS
 from synapse.crypto.keyring import Keyring
 from synapse.events.builder import EventBuilderFactory
 from synapse.events.spamcheck import SpamChecker
@@ -310,7 +310,7 @@ class HomeServer(object):
         return (
             InsecureInterceptableContextFactory()
             if self.config.use_insecure_ssl_client_just_for_testing_do_not_use
-            else BrowserLikePolicyForHTTPS()
+            else RegularPolicyForHTTPS()
         )
 
     def build_simple_http_client(self):
@@ -420,7 +420,7 @@ class HomeServer(object):
         return PusherPool(self)
 
     def build_http_client(self):
-        tls_client_options_factory = context_factory.ClientTLSOptionsFactory(
+        tls_client_options_factory = context_factory.FederationPolicyForHTTPS(
             self.config
         )
         return MatrixFederationHttpClient(self, tls_client_options_factory)

diff --git a/tests/config/test_tls.py b/tests/config/test_tls.py
index 1be6ff563..ec32d4b1c 100644
--- a/tests/config/test_tls.py
+++ b/tests/config/test_tls.py
@@ -23,7 +23,7 @@ from OpenSSL import SSL
 
 from synapse.config._base import Config, RootConfig
 from synapse.config.tls import ConfigError, TlsConfig
-from synapse.crypto.context_factory import ClientTLSOptionsFactory
+from synapse.crypto.context_factory import FederationPolicyForHTTPS
 
 from tests.unittest import TestCase
 
@@ -180,12 +180,13 @@ s4niecZKPBizL6aucT59CsunNmmb5Glq8rlAcU+1ZTZZzGYqVYhF6axB9Qg=
         t = TestConfig()
         t.read_config(config, config_dir_path="", data_dir_path="")
 
-        cf = ClientTLSOptionsFactory(t)
+        cf = FederationPolicyForHTTPS(t)
+        options = _get_ssl_context_options(cf._verify_ssl_context)
 
         # The context has had NO_TLSv1_1 and NO_TLSv1_0 set, but not NO_TLSv1_2
-        self.assertNotEqual(cf._verify_ssl._options & SSL.OP_NO_TLSv1, 0)
-        self.assertNotEqual(cf._verify_ssl._options & SSL.OP_NO_TLSv1_1, 0)
-        self.assertEqual(cf._verify_ssl._options & SSL.OP_NO_TLSv1_2, 0)
+        self.assertNotEqual(options & SSL.OP_NO_TLSv1, 0)
+        self.assertNotEqual(options & SSL.OP_NO_TLSv1_1, 0)
+        self.assertEqual(options & SSL.OP_NO_TLSv1_2, 0)
 
     def test_tls_client_minimum_set_passed_through_1_0(self):
         """
@@ -195,12 +196,13 @@ s4niecZKPBizL6aucT59CsunNmmb5Glq8rlAcU+1ZTZZzGYqVYhF6axB9Qg=
         t = TestConfig()
         t.read_config(config, config_dir_path="", data_dir_path="")
 
-        cf = ClientTLSOptionsFactory(t)
+        cf = FederationPolicyForHTTPS(t)
+        options = _get_ssl_context_options(cf._verify_ssl_context)
 
         # The context has not had any of the NO_TLS set.
-        self.assertEqual(cf._verify_ssl._options & SSL.OP_NO_TLSv1, 0)
-        self.assertEqual(cf._verify_ssl._options & SSL.OP_NO_TLSv1_1, 0)
-        self.assertEqual(cf._verify_ssl._options & SSL.OP_NO_TLSv1_2, 0)
+        self.assertEqual(options & SSL.OP_NO_TLSv1, 0)
+        self.assertEqual(options & SSL.OP_NO_TLSv1_1, 0)
+        self.assertEqual(options & SSL.OP_NO_TLSv1_2, 0)
 
     def test_acme_disabled_in_generated_config_no_acme_domain_provied(self):
         """
@@ -273,7 +275,7 @@ s4niecZKPBizL6aucT59CsunNmmb5Glq8rlAcU+1ZTZZzGYqVYhF6axB9Qg=
         t = TestConfig()
         t.read_config(config, config_dir_path="", data_dir_path="")
 
-        cf = ClientTLSOptionsFactory(t)
+        cf = FederationPolicyForHTTPS(t)
 
         # Not in the whitelist
         opts = cf.get_options(b"notexample.com")
@@ -282,3 +284,10 @@ s4niecZKPBizL6aucT59CsunNmmb5Glq8rlAcU+1ZTZZzGYqVYhF6axB9Qg=
         # Caught by the wildcard
         opts = cf.get_options(idna.encode("テスト.ドメイン.テスト"))
         self.assertFalse(opts._verifier._verify_certs)
+
+
+def _get_ssl_context_options(ssl_context: SSL.Context) -> int:
+    """get the options bits from an openssl context object"""
+    # the OpenSSL.SSL.Context wrapper doesn't expose get_options, so we have to
+    # use the low-level interface
+    return SSL._lib.SSL_CTX_get_options(ssl_context._context)
diff --git a/tests/http/federation/test_matrix_federation_agent.py b/tests/http/federation/test_matrix_federation_agent.py
index cfcd98ff7..fdc1d918f 100644
--- a/tests/http/federation/test_matrix_federation_agent.py
+++ b/tests/http/federation/test_matrix_federation_agent.py
@@ -31,7 +31,7 @@ from twisted.web.http_headers import Headers
 from twisted.web.iweb import IPolicyForHTTPS
 
 from synapse.config.homeserver import HomeServerConfig
-from synapse.crypto.context_factory import ClientTLSOptionsFactory
+from synapse.crypto.context_factory import FederationPolicyForHTTPS
 from synapse.http.federation.matrix_federation_agent import MatrixFederationAgent
 from synapse.http.federation.srv_resolver import Server
 from synapse.http.federation.well_known_resolver import (
@@ -79,7 +79,7 @@ class MatrixFederationAgentTests(unittest.TestCase):
         self._config = config = HomeServerConfig()
         config.parse_config_dict(config_dict, "", "")
 
-        self.tls_factory = ClientTLSOptionsFactory(config)
+        self.tls_factory = FederationPolicyForHTTPS(config)
 
         self.well_known_cache = TTLCache("test_cache", timer=self.reactor.seconds)
         self.had_well_known_cache = TTLCache("test_cache", timer=self.reactor.seconds)
@@ -715,7 +715,7 @@ class MatrixFederationAgentTests(unittest.TestCase):
         config = default_config("test", parse=True)
 
         # Build a new agent and WellKnownResolver with a different tls factory
-        tls_factory = ClientTLSOptionsFactory(config)
+        tls_factory = FederationPolicyForHTTPS(config)
         agent = MatrixFederationAgent(
             reactor=self.reactor,
             tls_client_options_factory=tls_factory,

OpenSSL contexts are not shared between non-federation connections
... ie, each connection to a sydent/sygnal/etc gets its own OpenSSL context
tests/config/test_tls.py::TLSConfigTests::test_acme_disabled_in_generated_config_no_acme_domain_provied tests/config/test_tls.py::TLSConfigTests::test_acme_enabled_in_generated_config_domain_provided tests/config/test_tls.py::TLSConfigTests::test_tls_client_minimum_1_point_3_exists tests/config/test_tls.py::TLSConfigTests::test_tls_client_minimum_1_point_3_missing tests/config/test_tls.py::TLSConfigTests::test_tls_client_minimum_default tests/config/test_tls.py::TLSConfigTests::test_tls_client_minimum_set tests/config/test_tls.py::TLSConfigTests::test_tls_client_minimum_set_passed_through_1_0 tests/config/test_tls.py::TLSConfigTests::test_tls_client_minimum_set_passed_through_1_2 tests/config/test_tls.py::TLSConfigTests::test_warn_self_signed tests/config/test_tls.py::TLSConfigTests::test_whitelist_idna_failure tests/config/test_tls.py::TLSConfigTests::test_whitelist_idna_result tests/http/federation/test_matrix_federation_agent.py::TestCachePeriodFromHeaders::test_cache_control tests/http/federation/test_matrix_federation_agent.py::TestCachePeriodFromHeaders::test_expires