diff --git a/synapse/http/client.py b/synapse/http/client.py
index 4abb479ae3..f3e4973c2e 100644
--- a/synapse/http/client.py
+++ b/synapse/http/client.py
@@ -18,6 +18,7 @@ from OpenSSL.SSL import VERIFY_NONE
 from synapse.api.errors import (
     CodeMessageException, MatrixCodeMessageException, SynapseError, Codes,
 )
+from synapse.util.caches import CACHE_SIZE_FACTOR
 from synapse.util.logcontext import make_deferred_yieldable
 from synapse.util import logcontext
 import synapse.metrics
@@ -30,6 +31,7 @@ from twisted.internet.endpoints import HostnameEndpoint, wrapClientTLS
 from twisted.web.client import (
     BrowserLikeRedirectAgent, ContentDecoderAgent, GzipDecoder, Agent,
     readBody, PartialDownloadError,
+    HTTPConnectionPool,
 )
 from twisted.web.client import FileBodyProducer as TwistedFileBodyProducer
 from twisted.web.http import PotentialDataLoss
@@ -64,13 +66,23 @@ class SimpleHttpClient(object):
     """
     def __init__(self, hs):
         self.hs = hs
+
+        pool = HTTPConnectionPool(reactor)
+
+        # the pusher makes lots of concurrent SSL connections to sygnal, and
+        # tends to do so in batches, so we need to allow the pool to keep lots
+        # of idle connections around.
+        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 = Agent(
             reactor,
             connectTimeout=15,
-            contextFactory=hs.get_http_client_context_factory()
+            contextFactory=hs.get_http_client_context_factory(),
+            pool=pool,
         )
         self.user_agent = hs.version_string
         self.clock = hs.get_clock()