diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
index 9c1c7ddba9..026a5abc25 100644
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -3,6 +3,7 @@
 from test.support import import_helper
 import binascii
 import copy
+import os
 import pickle
 import random
 import sys
@@ -18,6 +19,35 @@
         hasattr(zlib.decompressobj(), "copy"),
         'requires Decompress.copy()')
 
+# bpo-46623: On s390x, when a hardware accelerator is used, using different
+# ways to compress data with zlib can produce different compressed data.
+# Simplified test_pair() code:
+#
+#   def func1(data):
+#       return zlib.compress(data)
+#
+#   def func2(data)
+#       co = zlib.compressobj()
+#       x1 = co.compress(data)
+#       x2 = co.flush()
+#       return x1 + x2
+#
+# On s390x if zlib uses a hardware accelerator, func1() creates a single
+# "final" compressed block whereas func2() produces 3 compressed blocks (the
+# last one is a final block). On other platforms with no accelerator, func1()
+# and func2() produce the same compressed data made of a single (final)
+# compressed block.
+#
+# Only the compressed data is different, the decompression returns the original
+# data:
+#
+#   zlib.decompress(func1(data)) == zlib.decompress(func2(data)) == data
+#
+# Make the assumption that s390x always has an accelerator to simplify the skip
+# condition. Windows doesn't have os.uname() but it doesn't support s390x.
+skip_on_s390x = unittest.skipIf(hasattr(os, 'uname') and os.uname().machine == 's390x',
+                                'skipped on s390x')
+
 
 class VersionTestCase(unittest.TestCase):
 
@@ -184,6 +214,7 @@ def test_keywords(self):
                                          bufsize=zlib.DEF_BUF_SIZE),
                          HAMLET_SCENE)
 
+    @skip_on_s390x
     def test_speech128(self):
         # compress more data
         data = HAMLET_SCENE * 128
@@ -237,6 +268,7 @@ class CompressObjectTestCase(BaseCompressTestCase, unittest.TestCase):
     # TODO: RUSTPYTHON
     @unittest.expectedFailure
     # Test compression object
+    @skip_on_s390x
     def test_pair(self):
         # straightforward compress/decompress objects
         datasrc = HAMLET_SCENE * 128
@@ -853,6 +885,13 @@ def test_wbits(self):
         dco = zlib.decompressobj(32 + 15)
         self.assertEqual(dco.decompress(gzip), HAMLET_SCENE)
 
+        for wbits in (-15, 15, 31):
+            with self.subTest(wbits=wbits):
+                expected = HAMLET_SCENE
+                actual = zlib.decompress(
+                    zlib.compress(HAMLET_SCENE, wbits=wbits), wbits=wbits
+                )
+                self.assertEqual(expected, actual)
 
 def choose_lines(source, number, seed=None, generator=random):
     """Return a list of number lines randomly chosen from the source"""