diff --git a/Doc/library/zlib.rst b/Doc/library/zlib.rst
--- a/Doc/library/zlib.rst
+++ b/Doc/library/zlib.rst
@@ -71,9 +71,23 @@
    *method* is the compression algorithm. Currently, the only supported value is
    ``DEFLATED``.
 
-   *wbits* is the base two logarithm of the size of the window buffer. This
-   should be an integer from ``8`` to ``15``. Higher values give better
-   compression, but use more memory.
+   .. The following discussion of wbits is repeated under decompress().
+
+   *wbits* can take several ranges of values:
+
+   * +8 to +15: The base two logarithm of the size of the
+     history buffer (the "window size") used when compressing data.
+     The window size can therefore range between 256 and 32768.
+     Larger values resulting in better compression at the expense of greater
+     memory usage.  The resulting output will include a zlib-specific
+     header and trailer.
+
+   * -8 to -15: Uses the absolute value of *wbits* as the window size, while
+     producing a raw output stream with no header or trailer.
+
+   * +24 to +31 = 16 + (8 to 15): Uses the low 4 bits of the value as
+     the window size, while including a basic :program:`gzip` header
+     and trailer in the output.
 
    *memlevel* controls the amount of memory used for internal compression state.
    Valid values range from ``1`` to ``9``. Higher values using more memory,
@@ -124,15 +138,28 @@
    If *bufsize* is given, it is used as the initial size of the output
    buffer.  Raises the :exc:`error` exception if any error occurs.
 
-   The absolute value of *wbits* is the base two logarithm of the size of the
-   history buffer (the "window size") used when compressing data.  Its absolute
-   value should be between 8 and 15 for the most recent versions of the zlib
-   library, larger values resulting in better compression at the expense of greater
-   memory usage.  When decompressing a stream, *wbits* must not be smaller
+   .. The following discussion of wbits is repeated for compressobj.
+
+   *wbits* can take several ranges of values:
+
+   * +8 to +15: The base two logarithm of the size of the
+     history buffer (the "window size") used when compressing data.
+     The window size can therefore range between 256 and 32768.
+     Larger values resulting in better compression at the expense of greater
+     memory usage.  The resulting output will include a zlib-specific
+     header and trailer.
+
+   * -8 to -15: Uses the absolute value of *wbits* as the window size, while
+     producing a raw output stream with no header or trailer.
+
+   * +24 to +31 = 16 + (8 to 15): Uses the low 4 bits of the value as
+     the window size, while including a basic :program:`gzip` header
+     and trailer in the output.
+
+   When decompressing a stream, *wbits* must not be smaller
    than the size originally used to compress the stream; using a too-small
    value will result in an exception. The default value is therefore the
-   highest value, 15.  When *wbits* is negative, the standard
-   :program:`gzip` header is suppressed.
+   highest value, 15.
 
    *bufsize* is the initial size of the buffer used to hold decompressed data.  If
    more space is required, the buffer size will be increased as needed, so you
@@ -285,4 +312,3 @@
    http://www.zlib.net/manual.html
       The zlib manual explains  the semantics and usage of the library's many
       functions.
-