diff --git a/changelog.d/3587.misc b/changelog.d/3587.misc
new file mode 100644
index 000000000..75a347991
--- /dev/null
+++ b/changelog.d/3587.misc
@@ -0,0 +1 @@
+Improve logging for exceptions when handling PDUs
\ No newline at end of file
diff --git a/synapse/federation/federation_server.py b/synapse/federation/federation_server.py
index 48f26db67..e501251b6 100644
--- a/synapse/federation/federation_server.py
+++ b/synapse/federation/federation_server.py
@@ -24,6 +24,7 @@ from prometheus_client import Counter
 
 from twisted.internet import defer
 from twisted.internet.abstract import isIPAddress
+from twisted.python import failure
 
 from synapse.api.constants import EventTypes
 from synapse.api.errors import AuthError, FederationError, NotFoundError, SynapseError
@@ -186,8 +187,12 @@ class FederationServer(FederationBase):
                     logger.warn("Error handling PDU %s: %s", event_id, e)
                     pdu_results[event_id] = {"error": str(e)}
                 except Exception as e:
+                    f = failure.Failure()
                     pdu_results[event_id] = {"error": str(e)}
-                    logger.exception("Failed to handle PDU %s", event_id)
+                    logger.error(
+                        "Failed to handle PDU %s: %s",
+                        event_id, f.getTraceback().rstrip(),
+                    )
 
         yield async.concurrently_execute(
             process_pdus_for_room, pdus_by_room.keys(),
@@ -203,8 +208,8 @@ class FederationServer(FederationBase):
                 )
 
         pdu_failures = getattr(transaction, "pdu_failures", [])
-        for failure in pdu_failures:
-            logger.info("Got failure %r", failure)
+        for fail in pdu_failures:
+            logger.info("Got failure %r", fail)
 
         response = {
             "pdus": pdu_results,