diff --git a/Doc/library/zlib.rst b/Doc/library/zlib.rst
--- a/Doc/library/zlib.rst
+++ b/Doc/library/zlib.rst
@@ -71,12 +71,25 @@
    *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.
+   .. _wbits-description:
+
+   *wbits* controls the size of the history buffer (or the "window size")
+   used when compressing data, and can take several ranges of values:
+
+   * +8 to +15: The base two logarithm of the window size, which
+     therefore ranges between 256 and 32768.  Larger values produce
+     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 trailing checksum.
+
+   * +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 trailing checksum 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,
+   Valid values range from ``1`` to ``9``. Higher values use more memory,
    but are faster and produce smaller output.
 
    *strategy* is used to tune the compression algorithm. Possible values are
@@ -118,21 +131,20 @@
 
 .. function:: decompress(data[, wbits[, bufsize]])
 
-   Decompresses the bytes in *data*, returning a bytes object containing the
-   uncompressed data.  The *wbits* parameter controls the size of the window
-   buffer, and is discussed further below.
-   If *bufsize* is given, it is used as the initial size of the output
-   buffer.  Raises the :exc:`error` exception if any error occurs.
+   Decompresses the bytes in *data*, returning a bytes object
+   containing the uncompressed data.  The *wbits* parameter controls
+   the window size used for decompression.  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
-   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.
+   *wbits* controls the size of the history buffer (or the "window
+   size") used for decompressing the data and
+   `is described further <#wbits-description>`__ in the documentation for
+   :func:`compressobj`.  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 :exc:`error` exception. The default value
+   is therefore the 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
@@ -145,7 +157,13 @@
    Returns a decompression object, to be used for decompressing data streams that
    won't fit into memory at once.
 
-   The *wbits* parameter controls the size of the window buffer.
+   *wbits* controls the size of the history buffer (or the "window size")
+   used when compressing data, and `is described further <#wbits-description>`__
+   in the documentation for :func:`compressobj`. 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
+   :exc:`error` exception. The default value is therefore the highest
+   value, 15.
 
    The *zdict* parameter specifies a predefined compression dictionary. If
    provided, this must be the same dictionary as was used by the compressor that
@@ -285,4 +303,3 @@
    http://www.zlib.net/manual.html
       The zlib manual explains  the semantics and usage of the library's many
       functions.
-