diff --git a/Doc/library/unittest.rst b/Doc/library/unittest.rst
index 9e309088b49..609789f6c6a 100644
--- a/Doc/library/unittest.rst
+++ b/Doc/library/unittest.rst
@@ -1151,16 +1151,16 @@ Test cases
       .. deprecated:: 3.2
 
 
-   .. method:: assertCountEqual(actual, expected, msg=None)
+   .. method:: assertCountEqual(first, second, msg=None)
 
-      Test that sequence *actual* contains the same elements as *expected*,
+      Test that sequence *first* contains the same elements as *second*,
       regardless of their order. When they don't, an error message listing the
       differences between the sequences will be generated.
 
-      Duplicate elements are *not* ignored when comparing *actual* and
-      *expected*. It verifies if each element has the same count in both
+      Duplicate elements are *not* ignored when comparing *first* and
+      *second*. It verifies whether each element has the same count in both
       sequences. Equivalent to:
-      ``assertEqual(Counter(list(actual)), Counter(list(expected)))``
+      ``assertEqual(Counter(list(first)), Counter(list(second)))``
       but works with sequences of unhashable objects as well.
 
       .. versionadded:: 3.2
diff --git a/Lib/unittest/case.py b/Lib/unittest/case.py
index 82b139faf12..004a9f5d336 100644
--- a/Lib/unittest/case.py
+++ b/Lib/unittest/case.py
@@ -1004,20 +1004,20 @@ class TestCase(object):
             self.fail(self._formatMessage(msg, standardMsg))
 
 
-    def assertCountEqual(self, actual, expected, msg=None):
-        """An unordered sequence specific comparison. It asserts that
-        actual and expected have the same element counts.
-        Equivalent to::
+    def assertCountEqual(self, first, second, msg=None):
+        """An unordered sequence comparison asserting that the same elements,
+        regardless of order.  If the same element occurs more than once,
+        it verifies that the elements occur the same number of times.
 
-            self.assertEqual(Counter(list(actual)),
-                             Counter(list(expected)))
+            self.assertEqual(Counter(list(first)),
+                             Counter(list(second)))
 
-        Asserts that each element has the same count in both sequences.
-        Example:
+         Example:
             - [0, 1, 1] and [1, 0, 1] compare equal.
             - [0, 0, 1] and [0, 1] compare unequal.
+
         """
-        actual_seq, expected_seq = list(actual), list(expected)
+        actual_seq, expected_seq = list(first), list(second)
         try:
             actual = collections.Counter(actual_seq)
             expected = collections.Counter(expected_seq)
@@ -1031,7 +1031,7 @@ class TestCase(object):
 
         if differences:
             standardMsg = 'Element counts were not equal:\n'
-            lines = ['Got %d, expected %d:  %r' % diff for diff in differences]
+            lines = ['First has %d, Second has %d:  %r' % diff for diff in differences]
             diffMsg = '\n'.join(lines)
             standardMsg = self._truncateMessage(standardMsg, diffMsg)
             msg = self._formatMessage(msg, standardMsg)