diff --git a/Modules/_collectionsmodule.c b/Modules/_collectionsmodule.c
--- a/Modules/_collectionsmodule.c
+++ b/Modules/_collectionsmodule.c
@@ -1767,6 +1767,10 @@
     PyObject *newval = NULL;
     PyObject *key = NULL;
     PyObject *one = NULL;
+    PyObject *mapping_getitem = NULL;
+    PyObject *mapping_setitem = NULL;
+    PyObject *dict_getitem = NULL;
+    PyObject *dict_setitem = NULL;
 
     if (!PyArg_UnpackTuple(args, "_count_elements", 2, 2, &mapping, &iterable))
         return NULL;
@@ -1781,7 +1785,32 @@
         return NULL;
     }
 
-    if (PyDict_CheckExact(mapping)) {
+    /*  The fast path can be used whenever 
+     *  Counter.__getitem__ is dict.__getitem__ and
+     *  when Counter.__setitem__ is dict.__setitem__.
+     */
+    mapping_getitem = PyObject_GetAttrString((PyObject *)Py_TYPE(mapping), "__getitem__");
+    if (mapping_getitem == NULL) {
+        PyErr_Clear();
+        goto done;
+    }
+    dict_getitem = PyObject_GetAttrString((PyObject *)&PyDict_Type, "__getitem__");
+    if (dict_getitem == NULL) {
+        PyErr_Clear();
+        goto done;
+    }
+    mapping_setitem = PyObject_GetAttrString((PyObject *)Py_TYPE(mapping), "__setitem__");
+    if (mapping_setitem == NULL) {
+        PyErr_Clear();
+        goto done;
+    }
+    dict_setitem = PyObject_GetAttrString((PyObject *)&PyDict_Type, "__setitem__");
+    if (dict_setitem == NULL) {
+        PyErr_Clear();
+        goto done;
+    }
+
+    if (mapping_getitem == dict_getitem && mapping_setitem == dict_setitem) {
         while (1) {
             key = PyIter_Next(it);
             if (key == NULL)
@@ -1825,10 +1854,15 @@
         }
     }
 
+done:
     Py_DECREF(it);
     Py_XDECREF(key);
     Py_XDECREF(newval);
-    Py_DECREF(one);
+    Py_XDECREF(one);
+    Py_XDECREF(mapping_getitem);
+    Py_XDECREF(mapping_setitem);
+    Py_XDECREF(dict_getitem);
+    Py_XDECREF(dict_setitem);
     if (PyErr_Occurred())
         return NULL;
     Py_RETURN_NONE;