diff --git a/Doc/library/base64.rst b/Doc/library/base64.rst
index e346efb..7d1a6e0 100644
--- a/Doc/library/base64.rst
+++ b/Doc/library/base64.rst
@@ -16,8 +16,8 @@
 encoding algorithm is not the same as the :program:`uuencode` program.
 
 There are two interfaces provided by this module.  The modern interface supports
-encoding and decoding string objects using all three :rfc:`3548` defined
-alphabets (normal, URL-safe, and filesystem-safe).  The legacy
+encoding and decoding string objects using both base-64 alphabets defined
+in :rfc:`3548` (normal, and URL- and filesystem-safe).  The legacy
 interface provides for encoding and decoding to and from file-like objects as
 well as strings, but only using the Base64 standard alphabet.
 
@@ -26,7 +26,7 @@
 
 .. function:: b64encode(s[, altchars])
 
-   Encode a string use Base64.
+   Encode a string using Base64.
 
    *s* is the string to encode.  Optional *altchars* must be a string of at least
    length 2 (additional characters are ignored) which specifies an alternative
@@ -46,7 +46,8 @@
    alphabet used instead of the ``+`` and ``/`` characters.
 
    The decoded string is returned.  A :exc:`TypeError` is raised if *s* is
-   incorrectly padded.  Non-base64-alphabet characters are
+   incorrectly padded.  Characters that are neither
+   in the normal base-64 alphabet nor the alternative alphabet are
    discarded prior to the padding check.
 
 
@@ -62,14 +63,16 @@
 
 .. function:: urlsafe_b64encode(s)
 
-   Encode string *s* using a URL-safe alphabet, which substitutes ``-`` instead of
+   Encode string *s* using the URL- and filesystem-safe
+   alphabet, which substitutes ``-`` instead of
    ``+`` and ``_`` instead of ``/`` in the standard Base64 alphabet.  The result
    can still contain ``=``.
 
 
 .. function:: urlsafe_b64decode(s)
 
-   Decode string *s* using a URL-safe alphabet, which substitutes ``-`` instead of
+   Decode string *s* using the URL- and filesystem-safe
+   alphabet, which substitutes ``-`` instead of
    ``+`` and ``_`` instead of ``/`` in the standard Base64 alphabet.
 
 
diff --git a/Lib/base64.py b/Lib/base64.py
index 844907f..38bc61e 100755
--- a/Lib/base64.py
+++ b/Lib/base64.py
@@ -65,8 +65,9 @@
     alternative alphabet used instead of the '+' and '/' characters.
 
     The decoded string is returned.  A TypeError is raised if s is
-    incorrectly padded.  Non-base64-alphabet characters are discarded prior
-    to the padding check.
+    incorrectly padded.  Characters that are neither in the normal base-64
+    alphabet nor the alternative alphabet are discarded prior to the padding
+    check.
     """
     if altchars is not None:
         s = s.translate(string.maketrans(altchars[:2], '+/'))
@@ -87,9 +88,10 @@
 def standard_b64decode(s):
     """Decode a string encoded with the standard Base64 alphabet.
 
-    s is the string to decode.  The decoded string is returned.  A TypeError
-    is raised if the string is incorrectly padded or if there are non-alphabet
-    characters present in the string.
+    Argument s is the string to decode.  The decoded string is returned.  A
+    TypeError is raised if the string is incorrectly padded.  Characters that
+    are not in the standard alphabet are discarded prior to the padding
+    check.
     """
     return b64decode(s)
 
@@ -97,19 +99,20 @@
 _urlsafe_decode_translation = string.maketrans(b'-_', b'+/')
 
 def urlsafe_b64encode(s):
-    """Encode a string using a url-safe Base64 alphabet.
+    """Encode a string using the URL- and filesystem-safe Base64 alphabet.
 
-    s is the string to encode.  The encoded string is returned.  The alphabet
-    uses '-' instead of '+' and '_' instead of '/'.
+    Argument s is the string to encode.  The encoded string is returned.  The
+    alphabet uses '-' instead of '+' and '_' instead of '/'.
     """
     return b64encode(s).translate(_urlsafe_encode_translation)
 
 def urlsafe_b64decode(s):
-    """Decode a string encoded with the standard Base64 alphabet.
+    """Decode a string using the URL- and filesystem-safe Base64 alphabet.
 
-    s is the string to decode.  The decoded string is returned.  A TypeError
-    is raised if the string is incorrectly padded or if there are non-alphabet
-    characters present in the string.
+    Argument s is the string to decode.  The decoded string is returned.  A
+    TypeError is raised if the string is incorrectly padded.  Characters that
+    are not in the URL-safe base-64 alphabet, and are not a plus '+' or slash
+    '/', are discarded prior to the padding check.
 
     The alphabet uses '-' instead of '+' and '_' instead of '/'.
     """
@@ -267,7 +270,7 @@
     a lowercase alphabet is acceptable as input.  For security purposes, the
     default is False.
 
-    The decoded string is returned.  A TypeError is raised if s were
+    The decoded string is returned.  A TypeError is raised if s is
     incorrectly padded or if there are non-alphabet characters present in the
     string.
     """
diff --git a/Lib/test/test_base64.py b/Lib/test/test_base64.py
index 5dd283b..6e67dc0 100644
--- a/Lib/test/test_base64.py
+++ b/Lib/test/test_base64.py
@@ -153,6 +153,13 @@
                  (b'YWJj\nYWI=', b'abcab'))
         for bstr, res in tests:
             self.assertEqual(base64.b64decode(bstr), res)
+            self.assertEqual(base64.standard_b64decode(bstr), res)
+            self.assertEqual(base64.urlsafe_b64decode(bstr), res)
+
+        # Normal alphabet characters not discarded when alternative given
+        res = b'\xFB\xEF\xBE\xFF\xFF\xFF'
+        self.assertEqual(base64.b64decode(b'++[[//]]', b'[]'), res)
+        self.assertEqual(base64.urlsafe_b64decode(b'++--//__'), res)
 
     def test_b32encode(self):
         eq = self.assertEqual
@@ -220,6 +227,10 @@
         eq(base64.b16decode('0102abcdef', True), '\x01\x02\xab\xcd\xef')
         # Non-bytes
         eq(base64.b16decode(bytearray("0102ABCDEF")), '\x01\x02\xab\xcd\xef')
+        # Non-alphabet characters
+        self.assertRaises(TypeError, base64.b16decode, '0102AG')
+        # Incorrect "padding"
+        self.assertRaises(TypeError, base64.b16decode, '010')