diff --git a/synapse/api/errors.py b/synapse/api/errors.py
index 6074df292f..cf48829c8b 100644
--- a/synapse/api/errors.py
+++ b/synapse/api/errors.py
@@ -69,9 +69,6 @@ class CodeMessageException(RuntimeError):
         self.code = code
         self.msg = msg
 
-    def error_dict(self):
-        return cs_error(self.msg)
-
 
 class MatrixCodeMessageException(CodeMessageException):
     """An error from a general matrix endpoint, eg. from a proxied Matrix API call.
@@ -308,14 +305,6 @@ class LimitExceededError(SynapseError):
         )
 
 
-def cs_exception(exception):
-    if isinstance(exception, CodeMessageException):
-        return exception.error_dict()
-    else:
-        logger.error("Unknown exception type: %s", type(exception))
-        return {}
-
-
 def cs_error(msg, code=Codes.UNKNOWN, **kwargs):
     """ Utility method for constructing an error response for client-server
     interactions.
diff --git a/synapse/federation/federation_client.py b/synapse/federation/federation_client.py
index baa9c3586f..0b09f93ca9 100644
--- a/synapse/federation/federation_client.py
+++ b/synapse/federation/federation_client.py
@@ -488,7 +488,7 @@ class FederationClient(FederationBase):
             The [Deferred] result of callback, if it succeeds
 
         Raises:
-            CodeMessageException if the chosen remote server returns a 300/400 code.
+            SynapseError if the chosen remote server returns a 300/400 code.
 
             RuntimeError if no servers were reachable.
         """
@@ -504,9 +504,9 @@ class FederationClient(FederationBase):
                     "Failed to %s via %s: %s",
                     description, destination, e,
                 )
-            except CodeMessageException as e:
+            except HttpResponseException as e:
                 if not 500 <= e.code < 600:
-                    raise
+                    raise SynapseError.from_http_response_exception(e)
                 else:
                     logger.warn(
                         "Failed to %s via %s: %i %s",
@@ -543,7 +543,7 @@ class FederationClient(FederationBase):
             Deferred: resolves to a tuple of (origin (str), event (object))
             where origin is the remote homeserver which generated the event.
 
-            Fails with a ``CodeMessageException`` if the chosen remote server
+            Fails with a ``SynapseError`` if the chosen remote server
             returns a 300/400 code.
 
             Fails with a ``RuntimeError`` if no servers were reachable.
@@ -599,7 +599,7 @@ class FederationClient(FederationBase):
             giving the serer the event was sent to, ``state`` (?) and
             ``auth_chain``.
 
-            Fails with a ``CodeMessageException`` if the chosen remote server
+            Fails with a ``SynapseError`` if the chosen remote server
             returns a 300/400 code.
 
             Fails with a ``RuntimeError`` if no servers were reachable.
@@ -673,12 +673,17 @@ class FederationClient(FederationBase):
     @defer.inlineCallbacks
     def send_invite(self, destination, room_id, event_id, pdu):
         time_now = self._clock.time_msec()
-        code, content = yield self.transport_layer.send_invite(
-            destination=destination,
-            room_id=room_id,
-            event_id=event_id,
-            content=pdu.get_pdu_json(time_now),
-        )
+        try:
+            code, content = yield self.transport_layer.send_invite(
+                destination=destination,
+                room_id=room_id,
+                event_id=event_id,
+                content=pdu.get_pdu_json(time_now),
+            )
+        except HttpResponseException as e:
+            if e.code == 403:
+                raise SynapseError.from_http_response_exception(e)
+            raise
 
         pdu_dict = content["event"]
 
@@ -709,7 +714,7 @@ class FederationClient(FederationBase):
         Return:
             Deferred: resolves to None.
 
-            Fails with a ``CodeMessageException`` if the chosen remote server
+            Fails with a ``SynapseError`` if the chosen remote server
             returns a 300/400 code.
 
             Fails with a ``RuntimeError`` if no servers were reachable.
diff --git a/synapse/http/server.py b/synapse/http/server.py
index 1940c1c4f4..6dacb31037 100644
--- a/synapse/http/server.py
+++ b/synapse/http/server.py
@@ -36,7 +36,6 @@ from synapse.api.errors import (
     Codes,
     SynapseError,
     UnrecognizedRequestError,
-    cs_exception,
 )
 from synapse.http.request_metrics import requests_counter
 from synapse.util.caches import intern_dict
@@ -77,16 +76,13 @@ def wrap_json_request_handler(h):
     def wrapped_request_handler(self, request):
         try:
             yield h(self, request)
-        except CodeMessageException as e:
+        except SynapseError as e:
             code = e.code
-            if isinstance(e, SynapseError):
-                logger.info(
-                    "%s SynapseError: %s - %s", request, code, e.msg
-                )
-            else:
-                logger.exception(e)
+            logger.info(
+                "%s SynapseError: %s - %s", request, code, e.msg
+            )
             respond_with_json(
-                request, code, cs_exception(e), send_cors=True,
+                request, code, e.error_dict(), send_cors=True,
                 pretty_print=_request_user_agent_is_curl(request),
             )