diff --git a/Doc/library/zlib.rst b/Doc/library/zlib.rst
index ec60ea24db6627..793c90f3c4e7a4 100644
--- a/Doc/library/zlib.rst
+++ b/Doc/library/zlib.rst
@@ -47,7 +47,7 @@ The available exception and functions in this module are:
       platforms, use ``adler32(data) & 0xffffffff``.
 
 
-.. function:: compress(data, /, level=-1)
+.. function:: compress(data, /, level=-1, wbits=MAX_WBITS)
 
    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;
@@ -55,11 +55,35 @@ The available exception and functions in this module are:
    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).
+
+   .. _compress-wbits:
+
+   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,
+   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
+     better compression at the expense of greater memory usage.  The
+     resulting output will include a zlib-specific header and trailer.
+
+   * −9 to −15: Uses the absolute value of *wbits* as the
+     window size logarithm, while producing a raw output stream with no
+     header or trailing checksum.
+
+   * +25 to +31 = 16 + (9 to 15): Uses the low 4 bits of the value as the
+     window size logarithm, while including a basic :program:`gzip` header
+     and trailing checksum in the output.
+
    Raises the :exc:`error` exception if any error occurs.
 
    .. versionchanged:: 3.6
       *level* can now be used as a keyword parameter.
 
+   .. versionchanged:: 3.11
+      The *wbits* parameter is now available to set window bits and
+      compression type.
 
 .. function:: compressobj(level=-1, method=DEFLATED, wbits=MAX_WBITS, memLevel=DEF_MEM_LEVEL, strategy=Z_DEFAULT_STRATEGY[, zdict])
 
@@ -76,23 +100,9 @@ The available exception and functions in this module are:
    *method* is the compression algorithm. Currently, the only supported value is
    :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,
-   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
-     better compression at the expense of greater memory usage.  The
-     resulting output will include a zlib-specific header and trailer.
-
-   * −9 to −15: Uses the absolute value of *wbits* as the
-     window size logarithm, while producing a raw output stream with no
-     header or trailing checksum.
-
-   * +25 to +31 = 16 + (9 to 15): Uses the low 4 bits of the value as the
-     window size logarithm, while including a basic :program:`gzip` header
-     and trailing checksum in the output.
+   The *wbits* parameter controls the size of the history buffer (or the
+   "window size"), and what header and trailer format will be used. It has
+   the same meaning as `described for compress() <#compress-wbits>`__.
 
    The *memLevel* argument controls the amount of memory used for the
    internal compression state. Valid values range from ``1`` to ``9``.
diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
index 7f30cac64f71b9..252e8360e0189f 100644
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -825,6 +825,12 @@ def test_wbits(self):
         dco = zlib.decompressobj(32 + 15)
         self.assertEqual(dco.decompress(gzip), HAMLET_SCENE)
 
+        for wbits in (-15, 15, 31):
+            self.assertEqual(
+                zlib.decompress(
+                    zlib.compress(HAMLET_SCENE, wbits=wbits), wbits=wbits
+                ), HAMLET_SCENE)
+
 
 def choose_lines(source, number, seed=None, generator=random):
     """Return a list of number lines randomly chosen from the source"""
diff --git a/Misc/NEWS.d/next/Library/2021-03-24-09-40-02.bpo-43612.vMGZ4y.rst b/Misc/NEWS.d/next/Library/2021-03-24-09-40-02.bpo-43612.vMGZ4y.rst
new file mode 100644
index 00000000000000..e6fc88f45eea5e
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-03-24-09-40-02.bpo-43612.vMGZ4y.rst
@@ -0,0 +1,5 @@
+:func:`zlib.compress` now accepts a wbits parameter which allows users to
+compress data as a raw deflate block without zlib headers and trailers in
+one go. Previously this required instantiating a ``zlib.compressobj``. It
+also provides a faster alternative to ``gzip.compress`` when wbits=31 is
+used.
diff --git a/Modules/clinic/zlibmodule.c.h b/Modules/clinic/zlibmodule.c.h
index 14e955db64e729..e2a5fccd36c54f 100644
--- a/Modules/clinic/zlibmodule.c.h
+++ b/Modules/clinic/zlibmodule.c.h
@@ -3,7 +3,7 @@ preserve
 [clinic start generated code]*/
 
 PyDoc_STRVAR(zlib_compress__doc__,
-"compress($module, data, /, level=Z_DEFAULT_COMPRESSION)\n"
+"compress($module, data, /, level=Z_DEFAULT_COMPRESSION, wbits=MAX_WBITS)\n"
 "--\n"
 "\n"
 "Returns a bytes object containing compressed data.\n"
@@ -11,26 +11,29 @@ PyDoc_STRVAR(zlib_compress__doc__,
 "  data\n"
 "    Binary data to be compressed.\n"
 "  level\n"
-"    Compression level, in 0-9 or -1.");
+"    Compression level, in 0-9 or -1.\n"
+"  wbits\n"
+"    The window buffer size and container format.");
 
 #define ZLIB_COMPRESS_METHODDEF    \
     {"compress", (PyCFunction)(void(*)(void))zlib_compress, METH_FASTCALL|METH_KEYWORDS, zlib_compress__doc__},
 
 static PyObject *
-zlib_compress_impl(PyObject *module, Py_buffer *data, int level);
+zlib_compress_impl(PyObject *module, Py_buffer *data, int level, int wbits);
 
 static PyObject *
 zlib_compress(PyObject *module, PyObject *const *args, Py_ssize_t nargs, PyObject *kwnames)
 {
     PyObject *return_value = NULL;
-    static const char * const _keywords[] = {"", "level", NULL};
+    static const char * const _keywords[] = {"", "level", "wbits", NULL};
     static _PyArg_Parser _parser = {NULL, _keywords, "compress", 0};
-    PyObject *argsbuf[2];
+    PyObject *argsbuf[3];
     Py_ssize_t noptargs = nargs + (kwnames ? PyTuple_GET_SIZE(kwnames) : 0) - 1;
     Py_buffer data = {NULL, NULL};
     int level = Z_DEFAULT_COMPRESSION;
+    int wbits = MAX_WBITS;
 
-    args = _PyArg_UnpackKeywords(args, nargs, NULL, kwnames, &_parser, 1, 2, 0, argsbuf);
+    args = _PyArg_UnpackKeywords(args, nargs, NULL, kwnames, &_parser, 1, 3, 0, argsbuf);
     if (!args) {
         goto exit;
     }
@@ -44,12 +47,21 @@ zlib_compress(PyObject *module, PyObject *const *args, Py_ssize_t nargs, PyObjec
     if (!noptargs) {
         goto skip_optional_pos;
     }
-    level = _PyLong_AsInt(args[1]);
-    if (level == -1 && PyErr_Occurred()) {
+    if (args[1]) {
+        level = _PyLong_AsInt(args[1]);
+        if (level == -1 && PyErr_Occurred()) {
+            goto exit;
+        }
+        if (!--noptargs) {
+            goto skip_optional_pos;
+        }
+    }
+    wbits = _PyLong_AsInt(args[2]);
+    if (wbits == -1 && PyErr_Occurred()) {
         goto exit;
     }
 skip_optional_pos:
-    return_value = zlib_compress_impl(module, &data, level);
+    return_value = zlib_compress_impl(module, &data, level, wbits);
 
 exit:
     /* Cleanup for data */
@@ -803,4 +815,4 @@ zlib_crc32(PyObject *module, PyObject *const *args, Py_ssize_t nargs)
 #ifndef ZLIB_DECOMPRESS___DEEPCOPY___METHODDEF
     #define ZLIB_DECOMPRESS___DEEPCOPY___METHODDEF
 #endif /* !defined(ZLIB_DECOMPRESS___DEEPCOPY___METHODDEF) */
-/*[clinic end generated code: output=6736bae59fab268b input=a9049054013a1b77]*/
+/*[clinic end generated code: output=e3e8a6142ea045a7 input=a9049054013a1b77]*/
diff --git a/Modules/zlibmodule.c b/Modules/zlibmodule.c
index a537087d19d835..32132baf5d083e 100644
--- a/Modules/zlibmodule.c
+++ b/Modules/zlibmodule.c
@@ -205,13 +205,15 @@ zlib.compress
     /
     level: int(c_default="Z_DEFAULT_COMPRESSION") = Z_DEFAULT_COMPRESSION
         Compression level, in 0-9 or -1.
+    wbits: int(c_default="MAX_WBITS") = MAX_WBITS
+        The window buffer size and container format.
 
 Returns a bytes object containing compressed data.
 [clinic start generated code]*/
 
 static PyObject *
-zlib_compress_impl(PyObject *module, Py_buffer *data, int level)
-/*[clinic end generated code: output=d80906d73f6294c8 input=638d54b6315dbed3]*/
+zlib_compress_impl(PyObject *module, Py_buffer *data, int level, int wbits)
+/*[clinic end generated code: output=46bd152fadd66df2 input=c4d06ee5782a7e3f]*/
 {
     PyObject *RetVal = NULL;
     Py_ssize_t obuflen = DEF_BUF_SIZE;
@@ -227,7 +229,8 @@ zlib_compress_impl(PyObject *module, Py_buffer *data, int level)
     zst.zalloc = PyZlib_Malloc;
     zst.zfree = PyZlib_Free;
     zst.next_in = ibuf;
-    int err = deflateInit(&zst, level);
+    int err = deflateInit2(&zst, level, DEFLATED, wbits, DEF_MEM_LEVEL,
+                           Z_DEFAULT_STRATEGY);
 
     switch (err) {
     case Z_OK: