diff --git a/changelog.d/4690.bugfix b/changelog.d/4690.bugfix
new file mode 100644
index 0000000000..e4cfc5e413
--- /dev/null
+++ b/changelog.d/4690.bugfix
@@ -0,0 +1 @@
+Fix TaskStopped exceptions in logs when outbound requests time out.
\ No newline at end of file
diff --git a/synapse/http/__init__.py b/synapse/http/__init__.py
index a3f9e4f67c..d36bcd6336 100644
--- a/synapse/http/__init__.py
+++ b/synapse/http/__init__.py
@@ -15,8 +15,10 @@
 # limitations under the License.
 import re
 
+from twisted.internet import task
 from twisted.internet.defer import CancelledError
 from twisted.python import failure
+from twisted.web.client import FileBodyProducer
 
 from synapse.api.errors import SynapseError
 
@@ -47,3 +49,16 @@ def redact_uri(uri):
         r'\1<redacted>\3',
         uri
     )
+
+
+class QuieterFileBodyProducer(FileBodyProducer):
+    """Wrapper for FileBodyProducer that avoids CRITICAL errors when the connection drops.
+
+    Workaround for https://github.com/matrix-org/synapse/issues/4003 /
+    https://twistedmatrix.com/trac/ticket/6528
+    """
+    def stopProducing(self):
+        try:
+            FileBodyProducer.stopProducing(self)
+        except task.TaskStopped:
+            pass
diff --git a/synapse/http/client.py b/synapse/http/client.py
index 47a1f82ff0..ad454f4964 100644
--- a/synapse/http/client.py
+++ b/synapse/http/client.py
@@ -15,6 +15,7 @@
 # limitations under the License.
 
 import logging
+from io import BytesIO
 
 from six import text_type
 from six.moves import urllib
@@ -39,7 +40,11 @@ from twisted.web.http import PotentialDataLoss
 from twisted.web.http_headers import Headers
 
 from synapse.api.errors import Codes, HttpResponseException, SynapseError
-from synapse.http import cancelled_to_request_timed_out_error, redact_uri
+from synapse.http import (
+    QuieterFileBodyProducer,
+    cancelled_to_request_timed_out_error,
+    redact_uri,
+)
 from synapse.util.async_helpers import timeout_deferred
 from synapse.util.caches import CACHE_SIZE_FACTOR
 from synapse.util.logcontext import make_deferred_yieldable
@@ -246,7 +251,7 @@ class SimpleHttpClient(object):
             )
 
     @defer.inlineCallbacks
-    def request(self, method, uri, data=b'', headers=None):
+    def request(self, method, uri, data=None, headers=None):
         """
         Args:
             method (str): HTTP method to use.
@@ -265,11 +270,15 @@ class SimpleHttpClient(object):
         logger.info("Sending request %s %s", method, redact_uri(uri))
 
         try:
+            body_producer = None
+            if data is not None:
+                body_producer = QuieterFileBodyProducer(BytesIO(data))
+
             request_deferred = treq.request(
                 method,
                 uri,
                 agent=self.agent,
-                data=data,
+                data=body_producer,
                 headers=headers,
                 **self._extra_treq_args
             )
diff --git a/synapse/http/matrixfederationclient.py b/synapse/http/matrixfederationclient.py
index 3c24bf3805..1682c9af13 100644
--- a/synapse/http/matrixfederationclient.py
+++ b/synapse/http/matrixfederationclient.py
@@ -28,11 +28,10 @@ from canonicaljson import encode_canonical_json
 from prometheus_client import Counter
 from signedjson.sign import sign_json
 
-from twisted.internet import defer, protocol, task
+from twisted.internet import defer, protocol
 from twisted.internet.error import DNSLookupError
 from twisted.internet.task import _EPSILON, Cooperator
 from twisted.web._newclient import ResponseDone
-from twisted.web.client import FileBodyProducer
 from twisted.web.http_headers import Headers
 
 import synapse.metrics
@@ -44,6 +43,7 @@ from synapse.api.errors import (
     RequestSendFailed,
     SynapseError,
 )
+from synapse.http import QuieterFileBodyProducer
 from synapse.http.federation.matrix_federation_agent import MatrixFederationAgent
 from synapse.util.async_helpers import timeout_deferred
 from synapse.util.logcontext import make_deferred_yieldable
@@ -839,16 +839,3 @@ def encode_query_args(args):
     query_bytes = urllib.parse.urlencode(encoded_args, True)
 
     return query_bytes.encode('utf8')
-
-
-class QuieterFileBodyProducer(FileBodyProducer):
-    """Wrapper for FileBodyProducer that avoids CRITICAL errors when the connection drops.
-
-    Workaround for https://github.com/matrix-org/synapse/issues/4003 /
-    https://twistedmatrix.com/trac/ticket/6528
-    """
-    def stopProducing(self):
-        try:
-            FileBodyProducer.stopProducing(self)
-        except task.TaskStopped:
-            pass