diff --git a/jsonpatch.py b/jsonpatch.py
index d3fc26d..c6e9b64 100644
--- a/jsonpatch.py
+++ b/jsonpatch.py
@@ -859,19 +859,20 @@ def _item_replaced(self, path, key, item):
         }, pointer_cls=self.pointer_cls))
 
     def _compare_dicts(self, path, src, dst):
-        src_keys = set(src.keys())
-        dst_keys = set(dst.keys())
-        added_keys = dst_keys - src_keys
-        removed_keys = src_keys - dst_keys
-
-        for key in removed_keys:
-            self._item_removed(path, str(key), src[key])
-
-        for key in added_keys:
-            self._item_added(path, str(key), dst[key])
-
-        for key in src_keys & dst_keys:
-            self._compare_values(path, key, src[key], dst[key])
+        # removed keys
+        for key in src:
+            if key not in dst:
+                self._item_removed(path, str(key), src[key])
+
+        # added keys
+        for key in dst:
+            if key not in src:
+                self._item_added(path, str(key), dst[key])
+
+        # shared keys
+        for key in src:
+            if key in dst:
+                self._compare_values(path, key, src[key], dst[key])
 
     def _compare_lists(self, path, src, dst):
         len_src, len_dst = len(src), len(dst)