diff --git a/changelog.d/3591.misc b/changelog.d/3591.misc
new file mode 100644
index 000000000..f0137766a
--- /dev/null
+++ b/changelog.d/3591.misc
@@ -0,0 +1 @@
+Fix some random logcontext leaks.
\ No newline at end of file
diff --git a/synapse/handlers/appservice.py b/synapse/handlers/appservice.py
index ec9fe01a5..ee41aed69 100644
--- a/synapse/handlers/appservice.py
+++ b/synapse/handlers/appservice.py
@@ -23,6 +23,7 @@ from twisted.internet import defer
 
 import synapse
 from synapse.api.constants import EventTypes
+from synapse.metrics.background_process_metrics import run_as_background_process
 from synapse.util.logcontext import make_deferred_yieldable, run_in_background
 from synapse.util.metrics import Measure
 
@@ -106,7 +107,9 @@ class ApplicationServicesHandler(object):
                             yield self._check_user_exists(event.state_key)
 
                         if not self.started_scheduler:
-                            self.scheduler.start().addErrback(log_failure)
+                            def start_scheduler():
+                                return self.scheduler.start().addErrback(log_failure)
+                            run_as_background_process("as_scheduler", start_scheduler)
                             self.started_scheduler = True
 
                         # Fork off pushes to these services
diff --git a/synapse/handlers/initial_sync.py b/synapse/handlers/initial_sync.py
index fb11716eb..40e7580a6 100644
--- a/synapse/handlers/initial_sync.py
+++ b/synapse/handlers/initial_sync.py
@@ -148,13 +148,15 @@ class InitialSyncHandler(BaseHandler):
             try:
                 if event.membership == Membership.JOIN:
                     room_end_token = now_token.room_key
-                    deferred_room_state = self.state_handler.get_current_state(
-                        event.room_id
+                    deferred_room_state = run_in_background(
+                        self.state_handler.get_current_state,
+                        event.room_id,
                     )
                 elif event.membership == Membership.LEAVE:
                     room_end_token = "s%d" % (event.stream_ordering,)
-                    deferred_room_state = self.store.get_state_for_events(
-                        [event.event_id], None
+                    deferred_room_state = run_in_background(
+                        self.store.get_state_for_events,
+                        [event.event_id], None,
                     )
                     deferred_room_state.addCallback(
                         lambda states: states[event.event_id]
@@ -387,19 +389,21 @@ class InitialSyncHandler(BaseHandler):
                 receipts = []
             defer.returnValue(receipts)
 
-        presence, receipts, (messages, token) = yield defer.gatherResults(
-            [
-                run_in_background(get_presence),
-                run_in_background(get_receipts),
-                run_in_background(
-                    self.store.get_recent_events_for_room,
-                    room_id,
-                    limit=limit,
-                    end_token=now_token.room_key,
-                )
-            ],
-            consumeErrors=True,
-        ).addErrback(unwrapFirstError)
+        presence, receipts, (messages, token) = yield make_deferred_yieldable(
+            defer.gatherResults(
+                [
+                    run_in_background(get_presence),
+                    run_in_background(get_receipts),
+                    run_in_background(
+                        self.store.get_recent_events_for_room,
+                        room_id,
+                        limit=limit,
+                        end_token=now_token.room_key,
+                    )
+                ],
+                consumeErrors=True,
+            ).addErrback(unwrapFirstError),
+        )
 
         messages = yield filter_events_for_client(
             self.store, user_id, messages, is_peeking=is_peeking,
diff --git a/synapse/storage/events.py b/synapse/storage/events.py
index 392935cac..4d0706f23 100644
--- a/synapse/storage/events.py
+++ b/synapse/storage/events.py
@@ -39,7 +39,7 @@ from synapse.types import RoomStreamToken, get_domain_from_id
 from synapse.util.async import ObservableDeferred
 from synapse.util.caches.descriptors import cached, cachedInlineCallbacks
 from synapse.util.frozenutils import frozendict_json_encoder
-from synapse.util.logcontext import make_deferred_yieldable
+from synapse.util.logcontext import PreserveLoggingContext, make_deferred_yieldable
 from synapse.util.logutils import log_function
 from synapse.util.metrics import Measure
 
@@ -147,7 +147,8 @@ class _EventPeristenceQueue(object):
                     # callbacks on the deferred.
                     try:
                         ret = yield per_item_callback(item)
-                        item.deferred.callback(ret)
+                        with PreserveLoggingContext():
+                            item.deferred.callback(ret)
                     except Exception:
                         item.deferred.errback()
             finally:
diff --git a/synapse/storage/pusher.py b/synapse/storage/pusher.py
index cc273a57b..8443bd4c1 100644
--- a/synapse/storage/pusher.py
+++ b/synapse/storage/pusher.py
@@ -233,7 +233,7 @@ class PusherStore(PusherWorkerStore):
             )
 
             if newly_inserted:
-                self.runInteraction(
+                yield self.runInteraction(
                     "add_pusher",
                     self._invalidate_cache_and_stream,
                     self.get_if_user_has_pusher, (user_id,)