diff --git a/changelog.d/5347.misc b/changelog.d/5347.misc
new file mode 100644
index 0000000000..436245fb11
--- /dev/null
+++ b/changelog.d/5347.misc
@@ -0,0 +1,2 @@
+Various improvements to debug logging.
+
diff --git a/synapse/crypto/event_signing.py b/synapse/crypto/event_signing.py
index 1dfa727fcf..99a586655b 100644
--- a/synapse/crypto/event_signing.py
+++ b/synapse/crypto/event_signing.py
@@ -31,7 +31,11 @@ logger = logging.getLogger(__name__)
 def check_event_content_hash(event, hash_algorithm=hashlib.sha256):
     """Check whether the hash for this PDU matches the contents"""
     name, expected_hash = compute_content_hash(event.get_pdu_json(), hash_algorithm)
-    logger.debug("Expecting hash: %s", encode_base64(expected_hash))
+    logger.debug(
+        "Verifying content hash on %s (expecting: %s)",
+        event.event_id,
+        encode_base64(expected_hash),
+    )
 
     # some malformed events lack a 'hashes'. Protect against it being missing
     # or a weird type by basically treating it the same as an unhashed event.
diff --git a/synapse/crypto/keyring.py b/synapse/crypto/keyring.py
index 8e1d666db1..e94e71bdad 100644
--- a/synapse/crypto/keyring.py
+++ b/synapse/crypto/keyring.py
@@ -866,10 +866,6 @@ def _handle_key_deferred(verify_request):
 
     json_object = verify_request.json_object
 
-    logger.debug(
-        "Got key %s %s:%s for server %s, verifying"
-        % (key_id, verify_key.alg, verify_key.version, server_name)
-    )
     try:
         verify_signed_json(json_object, server_name, verify_key)
     except SignatureVerifyException as e:
diff --git a/synapse/federation/federation_client.py b/synapse/federation/federation_client.py
index d559605382..70573746d6 100644
--- a/synapse/federation/federation_client.py
+++ b/synapse/federation/federation_client.py
@@ -232,7 +232,8 @@ class FederationClient(FederationBase):
                 moving to the next destination. None indicates no timeout.
 
         Returns:
-            Deferred: Results in the requested PDU.
+            Deferred: Results in the requested PDU, or None if we were unable to find
+               it.
         """
 
         # TODO: Rate limit the number of times we try and get the same event.
@@ -257,7 +258,12 @@ class FederationClient(FederationBase):
                     destination, event_id, timeout=timeout,
                 )
 
-                logger.debug("transaction_data %r", transaction_data)
+                logger.debug(
+                    "retrieved event id %s from %s: %r",
+                    event_id,
+                    destination,
+                    transaction_data,
+                )
 
                 pdu_list = [
                     event_from_pdu_json(p, format_ver, outlier=outlier)
@@ -331,7 +337,11 @@ class FederationClient(FederationBase):
             )
 
             if failed_to_fetch:
-                logger.warn("Failed to get %r", failed_to_fetch)
+                logger.warning(
+                    "Failed to fetch missing state/auth events for %s: %s",
+                    room_id,
+                    failed_to_fetch
+                )
 
             event_map = {
                 ev.event_id: ev for ev in fetched_events