diff --git a/Doc/library/zlib.rst b/Doc/library/zlib.rst
index 3d742ab..8a531c9 100644
--- a/Doc/library/zlib.rst
+++ b/Doc/library/zlib.rst
@@ -51,9 +51,9 @@
 
    Compresses the bytes in *data*, returning a bytes object containing compressed data.
    *level* is an integer from ``0`` to ``9`` or ``-1`` controlling the level of compression;
-   ``1`` is fastest and produces the least compression, ``9`` is slowest and
-   produces the most.  ``0`` is no compression.  The default value is ``-1``
-   (Z_DEFAULT_COMPRESSION).  Z_DEFAULT_COMPRESSION represents a default
+   ``1`` (Z_BEST_SPEED) is fastest and produces the least compression, ``9`` (Z_BEST_COMPRESSION)
+   is slowest and produces the most.  ``0`` (Z_NO_COMPRESSION) is no compression.
+   The default value is ``-1`` (Z_DEFAULT_COMPRESSION).  Z_DEFAULT_COMPRESSION represents a default
    compromise between speed and compression (currently equivalent to level 6).
    Raises the :exc:`error` exception if any error occurs.
 
@@ -61,23 +61,25 @@
       *level* can now be used as a keyword parameter.
 
 
-.. function:: compressobj(level=-1, method=DEFLATED, wbits=15, memLevel=8, strategy=Z_DEFAULT_STRATEGY[, zdict])
+.. function:: compressobj(level=-1, method=DEFLATED, wbits=MAX_WBITS, memLevel=DEF_MEM_LEVEL, strategy=Z_DEFAULT_STRATEGY[, zdict])
 
    Returns a compression object, to be used for compressing data streams that won't
    fit into memory at once.
 
    *level* is the compression level -- an integer from ``0`` to ``9`` or ``-1``.
-   A value of ``1`` is fastest and produces the least compression, while a value of
-   ``9`` is slowest and produces the most. ``0`` is no compression. The default
-   value is ``-1`` (Z_DEFAULT_COMPRESSION). Z_DEFAULT_COMPRESSION represents a default
-   compromise between speed and compression (currently equivalent to level 6).
+   A value of ``1`` (Z_BEST_SPEED) is fastest and produces the least compression,
+   while a value of ``9`` (Z_BEST_COMPRESSION) is slowest and produces the most.
+   ``0`` (Z_NO_COMPRESSION) is no compression.  The default value is ``-1`` (Z_DEFAULT_COMPRESSION).
+   Z_DEFAULT_COMPRESSION represents a default compromise between speed and compression
+   (currently equivalent to level 6).
 
    *method* is the compression algorithm. Currently, the only supported value is
-   ``DEFLATED``.
+   :const:`DEFLATED`.
 
    The *wbits* argument controls the size of the history buffer (or the
    "window size") used when compressing data, and whether a header and
-   trailer is included in the output.  It can take several ranges of values:
+   trailer is included in the output.  It can take several ranges of values,
+   defaulting to ``15`` (MAX_WBITS):
 
    * +9 to +15: The base-two logarithm of the window size, which
      therefore ranges between 512 and 32768.  Larger values produce
@@ -97,7 +99,8 @@
    Higher values use more memory, but are faster and produce smaller output.
 
    *strategy* is used to tune the compression algorithm. Possible values are
-   ``Z_DEFAULT_STRATEGY``, ``Z_FILTERED``, and ``Z_HUFFMAN_ONLY``.
+   :const:`Z_DEFAULT_STRATEGY`, :const:`Z_FILTERED`, :const:`Z_HUFFMAN_ONLY`,
+   :const:`Z_RLE` (zlib 1.2.0.1) and :const:`Z_FIXED` (zlib 1.2.2.2).
 
    *zdict* is a predefined compression dictionary. This is a sequence of bytes
    (such as a :class:`bytes` object) containing subsequences that are expected
@@ -175,7 +178,7 @@
    .. versionchanged:: 3.6
       *wbits* and *bufsize* can be used as keyword arguments.
 
-.. function:: decompressobj(wbits=15[, zdict])
+.. function:: decompressobj(wbits=MAX_WBITS[, zdict])
 
    Returns a decompression object, to be used for decompressing data streams that
    won't fit into memory at once.
@@ -213,13 +216,13 @@
 
    All pending input is processed, and a bytes object containing the remaining compressed
    output is returned.  *mode* can be selected from the constants
-   :const:`Z_SYNC_FLUSH`,  :const:`Z_FULL_FLUSH`,  or  :const:`Z_FINISH`,
-   defaulting to :const:`Z_FINISH`.  :const:`Z_SYNC_FLUSH` and
-   :const:`Z_FULL_FLUSH` allow compressing further bytestrings of data, while
-   :const:`Z_FINISH` finishes the compressed stream and  prevents compressing any
-   more data.  After calling :meth:`flush` with *mode* set to :const:`Z_FINISH`,
-   the :meth:`compress` method cannot be called again; the only realistic action is
-   to delete the object.
+   :const:`Z_NO_FLUSH`, :const:`Z_PARTIAL_FLUSH`, :const:`Z_SYNC_FLUSH`,
+   :const:`Z_FULL_FLUSH`, :const:`Z_BLOCK` (zlib 1.2.3.4), or :const:`Z_FINISH`,
+   defaulting to :const:`Z_FINISH`.  Except :const:`Z_FINISH`, all constants
+   allow compressing further bytestrings of data, while :const:`Z_FINISH` finishes the
+   compressed stream and prevents compressing any more data.  After calling :meth:`flush`
+   with *mode* set to :const:`Z_FINISH`, the :meth:`compress` method cannot be called again;
+   the only realistic action is to delete the object.
 
 
 .. method:: Compress.copy()
diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
index db950fc..99aa89b 100644
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -434,7 +434,8 @@
     def test_flushes(self):
         # Test flush() with the various options, using all the
         # different levels in order to provide more variations.
-        sync_opt = ['Z_NO_FLUSH', 'Z_SYNC_FLUSH', 'Z_FULL_FLUSH']
+        sync_opt = ['Z_NO_FLUSH', 'Z_SYNC_FLUSH', 'Z_FULL_FLUSH',
+                    'Z_PARTIAL_FLUSH', 'Z_BLOCK']
         sync_opt = [getattr(zlib, opt) for opt in sync_opt
                     if hasattr(zlib, opt)]
         data = HAMLET_SCENE * 8
diff --git a/Misc/NEWS.d/next/Library/2018-03-06-00-19-41.bpo-32969.rGTKa0.rst b/Misc/NEWS.d/next/Library/2018-03-06-00-19-41.bpo-32969.rGTKa0.rst
new file mode 100644
index 0000000..a92307e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2018-03-06-00-19-41.bpo-32969.rGTKa0.rst
@@ -0,0 +1,2 @@
+Expose several missing constants in zlib and fix corresponding
+documentation.
diff --git a/Modules/zlibmodule.c b/Modules/zlibmodule.c
index cb2aae1..cd587b4 100644
--- a/Modules/zlibmodule.c
+++ b/Modules/zlibmodule.c
@@ -1361,18 +1361,33 @@
     PyModule_AddIntMacro(m, DEFLATED);
     PyModule_AddIntMacro(m, DEF_MEM_LEVEL);
     PyModule_AddIntMacro(m, DEF_BUF_SIZE);
+    // compression levels
+    PyModule_AddIntMacro(m, Z_NO_COMPRESSION);
     PyModule_AddIntMacro(m, Z_BEST_SPEED);
     PyModule_AddIntMacro(m, Z_BEST_COMPRESSION);
     PyModule_AddIntMacro(m, Z_DEFAULT_COMPRESSION);
+    // compression strategies
     PyModule_AddIntMacro(m, Z_FILTERED);
     PyModule_AddIntMacro(m, Z_HUFFMAN_ONLY);
+#ifdef Z_RLE // 1.2.0.1
+    PyModule_AddIntMacro(m, Z_RLE);
+#endif
+#ifdef Z_FIXED // 1.2.2.2
+    PyModule_AddIntMacro(m, Z_FIXED);
+#endif
     PyModule_AddIntMacro(m, Z_DEFAULT_STRATEGY);
-
-    PyModule_AddIntMacro(m, Z_FINISH);
+    // allowed flush values
     PyModule_AddIntMacro(m, Z_NO_FLUSH);
+    PyModule_AddIntMacro(m, Z_PARTIAL_FLUSH);
     PyModule_AddIntMacro(m, Z_SYNC_FLUSH);
     PyModule_AddIntMacro(m, Z_FULL_FLUSH);
-
+    PyModule_AddIntMacro(m, Z_FINISH);
+#ifdef Z_BLOCK // 1.2.0.5 for inflate, 1.2.3.4 for deflate
+    PyModule_AddIntMacro(m, Z_BLOCK);
+#endif
+#ifdef Z_TREES // 1.2.3.4, only for inflate
+    PyModule_AddIntMacro(m, Z_TREES);
+#endif
     ver = PyUnicode_FromString(ZLIB_VERSION);
     if (ver != NULL)
         PyModule_AddObject(m, "ZLIB_VERSION", ver);