diff --git a/changelog.d/7556.misc b/changelog.d/7556.misc
new file mode 100644
index 000000000..ed271f9de
--- /dev/null
+++ b/changelog.d/7556.misc
@@ -0,0 +1 @@
+Stop logging some expected HTTP request errors as exceptions.
diff --git a/synapse/app/generic_worker.py b/synapse/app/generic_worker.py
index d751c9772..a45c87621 100644
--- a/synapse/app/generic_worker.py
+++ b/synapse/app/generic_worker.py
@@ -26,7 +26,7 @@ from twisted.web.resource import NoResource
 
 import synapse
 import synapse.events
-from synapse.api.errors import SynapseError
+from synapse.api.errors import HttpResponseException, RequestSendFailed, SynapseError
 from synapse.api.urls import (
     CLIENT_API_PREFIX,
     FEDERATION_PREFIX,
@@ -202,9 +202,14 @@ class KeyUploadServlet(RestServlet):
             # is there.
             auth_headers = request.requestHeaders.getRawHeaders(b"Authorization", [])
             headers = {"Authorization": auth_headers}
-            result = await self.http_client.post_json_get_json(
-                self.main_uri + request.uri.decode("ascii"), body, headers=headers
-            )
+            try:
+                result = await self.http_client.post_json_get_json(
+                    self.main_uri + request.uri.decode("ascii"), body, headers=headers
+                )
+            except HttpResponseException as e:
+                raise e.to_synapse() from e
+            except RequestSendFailed as e:
+                raise SynapseError(502, "Failed to talk to master") from e
 
             return 200, result
         else:
diff --git a/synapse/handlers/federation.py b/synapse/handlers/federation.py
index 81d859f80..bb03cc9ad 100644
--- a/synapse/handlers/federation.py
+++ b/synapse/handlers/federation.py
@@ -40,6 +40,7 @@ from synapse.api.errors import (
     Codes,
     FederationDeniedError,
     FederationError,
+    HttpResponseException,
     RequestSendFailed,
     SynapseError,
 )
@@ -1036,6 +1037,12 @@ class FederationHandler(BaseHandler):
                     # TODO: We can probably do something more intelligent here.
                     return True
                 except SynapseError as e:
+                    logger.info("Failed to backfill from %s because %s", dom, e)
+                    continue
+                except HttpResponseException as e:
+                    if 400 <= e.code < 500:
+                        raise e.to_synapse_error()
+
                     logger.info("Failed to backfill from %s because %s", dom, e)
                     continue
                 except CodeMessageException as e:
diff --git a/synapse/http/matrixfederationclient.py b/synapse/http/matrixfederationclient.py
index 44077f534..2d47b9ea0 100644
--- a/synapse/http/matrixfederationclient.py
+++ b/synapse/http/matrixfederationclient.py
@@ -144,6 +144,11 @@ def _handle_json_response(reactor, timeout_sec, request, response):
         d = timeout_deferred(d, timeout=timeout_sec, reactor=reactor)
 
         body = yield make_deferred_yieldable(d)
+    except TimeoutError as e:
+        logger.warning(
+            "{%s} [%s] Timed out reading response", request.txn_id, request.destination,
+        )
+        raise RequestSendFailed(e, can_retry=True) from e
     except Exception as e:
         logger.warning(
             "{%s} [%s] Error reading response: %s",
@@ -424,6 +429,8 @@ class MatrixFederationHttpClient(object):
                             )
 
                             response = yield request_deferred
+                    except TimeoutError as e:
+                        raise RequestSendFailed(e, can_retry=True) from e
                     except DNSLookupError as e:
                         raise_from(RequestSendFailed(e, can_retry=retry_on_dns_fail), e)
                     except Exception as e: