diff --git a/Doc/library/binascii.rst b/Doc/library/binascii.rst
index ffea2324a67..ece08198435 100644
--- a/Doc/library/binascii.rst
+++ b/Doc/library/binascii.rst
@@ -113,8 +113,25 @@ The :mod:`binascii` module defines the following functions:
       print binascii.crc32("hello world")
       # Or, in two pieces:
       crc = binascii.crc32("hello")
-      crc = binascii.crc32(" world", crc)
-      print crc
+      crc = binascii.crc32(" world", crc) & 0xffffffff
+      print 'crc32 = 0x%08x' % crc
+
+.. note::
+   To generate the same numeric value across all Python versions and
+   platforms use crc32(data) & 0xffffffff.  If you are only using
+   the checksum in packed binary format this is not necessary as the
+   return value will have the correct 32bit binary representation
+   regardless of sign.
+
+.. versionchanged:: 2.6
+   The return value will always be in the range [-2**31, 2**31-1]
+   regardless of platform.  In the past the value would be signed on
+   some platforms and unsigned on others.  Use & 0xffffffff on the
+   value if you want it to match 3.0 behavior.
+
+.. versionchanged:: 3.0
+   The return value will always be unsigned and in the range [0, 2**32-1]
+   regardless of platform.
 
 
 .. function:: b2a_hex(data)
diff --git a/Doc/library/zlib.rst b/Doc/library/zlib.rst
index 6ce4e661c16..ca55a5f19e2 100644
--- a/Doc/library/zlib.rst
+++ b/Doc/library/zlib.rst
@@ -31,22 +31,34 @@ The available exception and functions in this module are:
    Exception raised on compression and decompression errors.
 
 
-.. function:: adler32(string[, value])
+.. function:: adler32(data[, value])
 
-   Computes a Adler-32 checksum of *string*.  (An Adler-32 checksum is almost as
+   Computes a Adler-32 checksum of *data*.  (An Adler-32 checksum is almost as
    reliable as a CRC32 but can be computed much more quickly.)  If *value* is
    present, it is used as the starting value of the checksum; otherwise, a fixed
    default value is used.  This allows computing a running checksum over the
-   concatenation of several input strings.  The algorithm is not cryptographically
+   concatenation of several inputs.  The algorithm is not cryptographically
    strong, and should not be used for authentication or digital signatures.  Since
    the algorithm is designed for use as a checksum algorithm, it is not suitable
    for use as a general hash algorithm.
 
    This function always returns an integer object.
 
-   .. versionchanged:: 2.6
-     For consistent cross-platform behavior we always return a signed integer.
-     ie: Results in the (2**31)...(2**32-1) range will be negative.
+.. note::
+   To generate the same numeric value across all Python versions and
+   platforms use adler32(data) & 0xffffffff.  If you are only using
+   the checksum in packed binary format this is not necessary as the
+   return value will have the correct 32bit binary representation
+   regardless of sign.
+
+.. versionchanged:: 2.6
+   The return value will always be in the range [-2**31, 2**31-1]
+   regardless of platform.  In older versions the value would be
+   signed on some platforms and unsigned on others.
+
+.. versionchanged:: 3.0
+   The return value will always be unsigned and in the range [0, 2**32-1]
+   regardless of platform.
 
 
 .. function:: compress(string[, level])
@@ -66,25 +78,37 @@ The available exception and functions in this module are:
    ``9`` is slowest and produces the most.  The default value is ``6``.
 
 
-.. function:: crc32(string[, value])
+.. function:: crc32(data[, value])
 
    .. index::
       single: Cyclic Redundancy Check
       single: checksum; Cyclic Redundancy Check
 
-   Computes a CRC (Cyclic Redundancy Check)  checksum of *string*. If *value* is
+   Computes a CRC (Cyclic Redundancy Check)  checksum of *data*. If *value* is
    present, it is used as the starting value of the checksum; otherwise, a fixed
    default value is used.  This allows computing a running checksum over the
-   concatenation of several input strings.  The algorithm is not cryptographically
+   concatenation of several inputs.  The algorithm is not cryptographically
    strong, and should not be used for authentication or digital signatures.  Since
    the algorithm is designed for use as a checksum algorithm, it is not suitable
    for use as a general hash algorithm.
 
    This function always returns an integer object.
 
-   .. versionchanged:: 2.6
-     For consistent cross-platform behavior we always return a signed integer.
-     ie: Results in the (2**31)...(2**32-1) range will be negative.
+.. note::
+   To generate the same numeric value across all Python versions and
+   platforms use crc32(data) & 0xffffffff.  If you are only using
+   the checksum in packed binary format this is not necessary as the
+   return value will have the correct 32bit binary representation
+   regardless of sign.
+
+.. versionchanged:: 2.6
+   The return value will always be in the range [-2**31, 2**31-1]
+   regardless of platform.  In older versions the value would be
+   signed on some platforms and unsigned on others.
+
+.. versionchanged:: 3.0
+   The return value will always be unsigned and in the range [0, 2**32-1]
+   regardless of platform.
 
 
 .. function:: decompress(string[, wbits[, bufsize]])