diff --git a/Doc/library/tarfile.rst b/Doc/library/tarfile.rst
index f5c49b0ac4f..f9d34def79a 100644
--- a/Doc/library/tarfile.rst
+++ b/Doc/library/tarfile.rst
@@ -98,8 +98,8 @@ Some facts and figures:
    If *fileobj* is specified, it is used as an alternative to a :term:`file object`
    opened in binary mode for *name*. It is supposed to be at position 0.
 
-   For modes ``'w:gz'``, ``'r:gz'``, ``'w:bz2'``, ``'r:bz2'``, ``'x:gz'``,
-   ``'x:bz2'``, :func:`tarfile.open` accepts the keyword argument
+   For modes ``'w:gz'``, ``'x:gz'``, ``'w|gz'``, ``'w:bz2'``, ``'x:bz2'``,
+   ``'w|bz2'``, :func:`tarfile.open` accepts the keyword argument
    *compresslevel* (default ``9``) to specify the compression level of the file.
 
    For modes ``'w:xz'`` and ``'x:xz'``, :func:`tarfile.open` accepts the
@@ -152,6 +152,9 @@ Some facts and figures:
    .. versionchanged:: 3.6
       The *name* parameter accepts a :term:`path-like object`.
 
+   .. versionchanged:: 3.12
+      The *compresslevel* keyword argument also works for streams.
+
 
 .. class:: TarFile
    :noindex:
diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 169c88d63f7..a08f247f496 100755
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -336,7 +336,8 @@ class _Stream:
        _Stream is intended to be used only internally.
     """
 
-    def __init__(self, name, mode, comptype, fileobj, bufsize):
+    def __init__(self, name, mode, comptype, fileobj, bufsize,
+                 compresslevel):
         """Construct a _Stream object.
         """
         self._extfileobj = True
@@ -371,7 +372,7 @@ def __init__(self, name, mode, comptype, fileobj, bufsize):
                     self._init_read_gz()
                     self.exception = zlib.error
                 else:
-                    self._init_write_gz()
+                    self._init_write_gz(compresslevel)
 
             elif comptype == "bz2":
                 try:
@@ -383,7 +384,7 @@ def __init__(self, name, mode, comptype, fileobj, bufsize):
                     self.cmp = bz2.BZ2Decompressor()
                     self.exception = OSError
                 else:
-                    self.cmp = bz2.BZ2Compressor()
+                    self.cmp = bz2.BZ2Compressor(compresslevel)
 
             elif comptype == "xz":
                 try:
@@ -410,13 +411,14 @@ def __del__(self):
         if hasattr(self, "closed") and not self.closed:
             self.close()
 
-    def _init_write_gz(self):
+    def _init_write_gz(self, compresslevel):
         """Initialize for writing with gzip compression.
         """
-        self.cmp = self.zlib.compressobj(9, self.zlib.DEFLATED,
-                                            -self.zlib.MAX_WBITS,
-                                            self.zlib.DEF_MEM_LEVEL,
-                                            0)
+        self.cmp = self.zlib.compressobj(compresslevel,
+                                         self.zlib.DEFLATED,
+                                         -self.zlib.MAX_WBITS,
+                                         self.zlib.DEF_MEM_LEVEL,
+                                         0)
         timestamp = struct.pack("<L", int(time.time()))
         self.__write(b"\037\213\010\010" + timestamp + b"\002\377")
         if self.name.endswith(".gz"):
@@ -1659,7 +1661,9 @@ def not_compressed(comptype):
             if filemode not in ("r", "w"):
                 raise ValueError("mode must be 'r' or 'w'")
 
-            stream = _Stream(name, filemode, comptype, fileobj, bufsize)
+            compresslevel = kwargs.pop("compresslevel", 9)
+            stream = _Stream(name, filemode, comptype, fileobj, bufsize,
+                             compresslevel)
             try:
                 t = cls(name, filemode, stream, **kwargs)
             except:
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index e0389c5dc47..04f9bee66ce 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -1554,6 +1554,74 @@ class Bz2StreamWriteTest(Bz2Test, StreamWriteTest):
 class LzmaStreamWriteTest(LzmaTest, StreamWriteTest):
     decompressor = lzma.LZMADecompressor if lzma else None
 
+class _CompressedWriteTest(TarTest):
+    # This is not actually a standalone test.
+    # It does not inherit WriteTest because it only makes sense with gz,bz2
+    source = (b"And we move to Bristol where they have a special, " +
+              b"Very Silly candidate")
+
+    def _compressed_tar(self, compresslevel):
+        fobj = io.BytesIO()
+        with tarfile.open(tmpname, self.mode, fobj,
+                          compresslevel=compresslevel) as tarfl:
+            tarfl.addfile(tarfile.TarInfo("foo"), io.BytesIO(self.source))
+        return fobj
+
+    def _test_bz2_header(self, compresslevel):
+        fobj = self._compressed_tar(compresslevel)
+        self.assertEqual(fobj.getvalue()[0:10],
+                         b"BZh%d1AY&SY" % compresslevel)
+
+    def _test_gz_header(self, compresslevel):
+        fobj = self._compressed_tar(compresslevel)
+        self.assertEqual(fobj.getvalue()[:3], b"\x1f\x8b\x08")
+
+class Bz2CompressWriteTest(Bz2Test, _CompressedWriteTest, unittest.TestCase):
+    prefix = "w:"
+    def test_compression_levels(self):
+        self._test_bz2_header(1)
+        self._test_bz2_header(5)
+        self._test_bz2_header(9)
+
+class Bz2CompressStreamWriteTest(Bz2Test, _CompressedWriteTest,
+        unittest.TestCase):
+    prefix = "w|"
+    def test_compression_levels(self):
+        self._test_bz2_header(1)
+        self._test_bz2_header(5)
+        self._test_bz2_header(9)
+
+class GzCompressWriteTest(GzipTest,  _CompressedWriteTest, unittest.TestCase):
+    prefix = "w:"
+    def test_compression_levels(self):
+        self._test_gz_header(1)
+        self._test_gz_header(5)
+        self._test_gz_header(9)
+
+class GzCompressStreamWriteTest(GzipTest, _CompressedWriteTest,
+        unittest.TestCase):
+    prefix = "w|"
+    def test_compression_levels(self):
+        self._test_gz_header(1)
+        self._test_gz_header(5)
+        self._test_gz_header(9)
+
+class CompressLevelRaises(unittest.TestCase):
+    def test_compresslevel_wrong_modes(self):
+        compresslevel = 5
+        fobj = io.BytesIO()
+        with self.assertRaises(TypeError):
+            tarfile.open(tmpname, "w:", fobj, compresslevel=compresslevel)
+
+    def test_wrong_compresslevels(self):
+        # BZ2 checks that the compresslevel is in [1,9]. gz does not
+        fobj = io.BytesIO()
+        with self.assertRaises(ValueError):
+            tarfile.open(tmpname, "w:bz2", fobj, compresslevel=0)
+        with self.assertRaises(ValueError):
+            tarfile.open(tmpname, "w:bz2", fobj, compresslevel=10)
+        with self.assertRaises(ValueError):
+            tarfile.open(tmpname, "w|bz2", fobj, compresslevel=10)
 
 class GNUWriteTest(unittest.TestCase):
     # This testcase checks for correct creation of GNU Longname
diff --git a/Misc/NEWS.d/next/Library/2017-07-31-13-35-28.bpo-26253.8v_sCs.rst b/Misc/NEWS.d/next/Library/2017-07-31-13-35-28.bpo-26253.8v_sCs.rst
new file mode 100644
index 00000000000..fa0dc95b7d6
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2017-07-31-13-35-28.bpo-26253.8v_sCs.rst
@@ -0,0 +1,2 @@
+Allow adjustable compression level for tarfile streams in
+:func:`tarfile.open`.