diff --git a/Lib/base64.py b/Lib/base64.py
index 58f6ad6..eb8f258 100755
--- a/Lib/base64.py
+++ b/Lib/base64.py
@@ -541,7 +541,8 @@
 def encodestring(s):
     """Legacy alias of encodebytes()."""
     import warnings
-    warnings.warn("encodestring() is a deprecated alias, use encodebytes()",
+    warnings.warn("encodestring() is a deprecated alias since 3.1, "
+                  "use encodebytes()",
                   DeprecationWarning, 2)
     return encodebytes(s)
 
@@ -554,7 +555,8 @@
 def decodestring(s):
     """Legacy alias of decodebytes()."""
     import warnings
-    warnings.warn("decodestring() is a deprecated alias, use decodebytes()",
+    warnings.warn("decodestring() is a deprecated alias since Python 3.1, "
+                  "use decodebytes()",
                   DeprecationWarning, 2)
     return decodebytes(s)
 
diff --git a/Lib/test/test_base64.py b/Lib/test/test_base64.py
index 4f86aaa..4754739 100644
--- a/Lib/test/test_base64.py
+++ b/Lib/test/test_base64.py
@@ -18,6 +18,14 @@
         int_data = memoryview(b"1234").cast('I')
         self.assertRaises(TypeError, f, int_data)
 
+    def test_encodestring_warns(self):
+        with self.assertWarns(DeprecationWarning):
+            base64.encodestring(b"www.python.org")
+
+    def test_decodestring_warns(self):
+        with self.assertWarns(DeprecationWarning):
+            base64.decodestring(b"d3d3LnB5dGhvbi5vcmc=\n")
+
     def test_encodebytes(self):
         eq = self.assertEqual
         eq(base64.encodebytes(b"www.python.org"), b"d3d3LnB5dGhvbi5vcmc=\n")