diff --git a/synapse/api/auth.py b/synapse/api/auth.py
index bd2f058e4a..ee52ff66d4 100644
--- a/synapse/api/auth.py
+++ b/synapse/api/auth.py
@@ -261,12 +261,12 @@ class Auth(object):
             elif target_user_id != event.user_id:
                 kick_level = self._get_named_level(auth_events, "kick", 50)
 
-                if user_level < kick_level or user_level < target_level:
+                if user_level < kick_level or user_level <= target_level:
                     raise AuthError(
                         403, "You cannot kick user %s." % target_user_id
                     )
         elif Membership.BAN == membership:
-            if user_level < ban_level or user_level < target_level:
+            if user_level < ban_level or user_level <= target_level:
                 raise AuthError(403, "You don't have permission to ban")
         else:
             raise AuthError(500, "Unknown membership %s" % membership)
@@ -576,25 +576,25 @@ class Auth(object):
 
         # Check other levels:
         levels_to_check = [
-            ("users_default", []),
-            ("events_default", []),
-            ("ban", []),
-            ("redact", []),
-            ("kick", []),
-            ("invite", []),
+            ("users_default", None),
+            ("events_default", None),
+            ("ban", None),
+            ("redact", None),
+            ("kick", None),
+            ("invite", None),
         ]
 
         old_list = current_state.content.get("users")
         for user in set(old_list.keys() + user_list.keys()):
             levels_to_check.append(
-                (user, ["users"])
+                (user, "users")
             )
 
         old_list = current_state.content.get("events")
         new_list = event.content.get("events")
         for ev_id in set(old_list.keys() + new_list.keys()):
             levels_to_check.append(
-                (ev_id, ["events"])
+                (ev_id, "events")
             )
 
         old_state = current_state.content
@@ -602,12 +602,10 @@ class Auth(object):
 
         for level_to_check, dir in levels_to_check:
             old_loc = old_state
-            for d in dir:
-                old_loc = old_loc.get(d, {})
-
             new_loc = new_state
-            for d in dir:
-                new_loc = new_loc.get(d, {})
+            if dir:
+                old_loc = old_loc.get(dir, {})
+                new_loc = new_loc.get(dir, {})
 
             if level_to_check in old_loc:
                 old_level = int(old_loc[level_to_check])
@@ -623,6 +621,14 @@ class Auth(object):
                 if new_level == old_level:
                     continue
 
+            if dir == "users" and level_to_check != event.user_id:
+                if old_level == user_level:
+                    raise AuthError(
+                        403,
+                        "You don't have permission to remove ops level equal "
+                        "to your own"
+                    )
+
             if old_level > user_level or new_level > user_level:
                 raise AuthError(
                     403,