diff --git a/synapse/storage/state.py b/synapse/storage/state.py
index 2b325e1c1..ffa424603 100644
--- a/synapse/storage/state.py
+++ b/synapse/storage/state.py
@@ -240,6 +240,9 @@ class StateGroupWorkerStore(SQLBaseStore):
                     (
                         "AND type = ? AND state_key = ?",
                         (etype, state_key)
+                    ) if state_key is not None else (
+                        "AND type = ?",
+                        (etype,)
                     )
                     for etype, state_key in types
                 ]
@@ -259,10 +262,19 @@ class StateGroupWorkerStore(SQLBaseStore):
                         key = (typ, state_key)
                         results[group][key] = event_id
         else:
+            where_args = []
+            where_clauses = []
+            wildcard_types = False
             if types is not None:
-                where_clause = "AND (%s)" % (
-                    " OR ".join(["(type = ? AND state_key = ?)"] * len(types)),
-                )
+                for typ in types:
+                    if typ[1] is None:
+                        where_clauses.append("(type = ?)")
+                        where_args.extend(typ[0])
+                        wildcard_types = True
+                    else:
+                        where_clauses.append("(type = ? AND state_key = ?)")
+                        where_args.extend([typ[0], typ[1]])
+                where_clause = "AND (%s)" % (" OR ".join(where_clauses))
             else:
                 where_clause = ""
 
@@ -279,7 +291,7 @@ class StateGroupWorkerStore(SQLBaseStore):
                     # after we finish deduping state, which requires this func)
                     args = [next_group]
                     if types:
-                        args.extend(i for typ in types for i in typ)
+                        args.extend(where_args)
 
                     txn.execute(
                         "SELECT type, state_key, event_id FROM state_groups_state"
@@ -292,9 +304,17 @@ class StateGroupWorkerStore(SQLBaseStore):
                         if (typ, state_key) not in results[group]
                     )
 
-                    # If the lengths match then we must have all the types,
-                    # so no need to go walk further down the tree.
-                    if types is not None and len(results[group]) == len(types):
+                    # If the number of entries in the (type,state_key)->event_id dict
+                    # matches the number of (type,state_keys) types we were searching
+                    # for, then we must have found them all, so no need to go walk
+                    # further down the tree... UNLESS our types filter contained
+                    # wildcards (i.e. Nones) in which case we have to do an exhaustive
+                    # search
+                    if (
+                        types is not None and
+                        not wildcard_types and
+                        len(results[group]) == len(types)
+                    ):
                         break
 
                     next_group = self._simple_select_one_onecol_txn(