diff --git a/Lib/test/support/__init__.py b/Lib/test/support/__init__.py
index 78f410e1455..ba57eb307c0 100644
--- a/Lib/test/support/__init__.py
+++ b/Lib/test/support/__init__.py
@@ -2450,9 +2450,9 @@ else:
     else:
         C_RECURSION_LIMIT = 10000
 
-#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')
+# Windows doesn't have os.uname() but it doesn't support s390x.
+is_s390x = hasattr(os, 'uname') and os.uname().machine == 's390x'
+skip_on_s390x = unittest.skipIf(is_s390x, 'skipped on s390x')
 
 _BASE_COPY_SRC_DIR_IGNORED_NAMES = frozenset({
     # SRC_DIR/.git
diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
index 0a13986a847..8654b93ec64 100644
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -7,7 +7,7 @@ import os
 import pickle
 import random
 import sys
-from test.support import bigmemtest, _1G, _4G, skip_on_s390x
+from test.support import bigmemtest, _1G, _4G, is_s390x
 
 
 zlib = import_helper.import_module('zlib')
@@ -34,8 +34,9 @@ def _zlib_runtime_version_tuple(zlib_version=zlib.ZLIB_RUNTIME_VERSION):
 ZLIB_RUNTIME_VERSION_TUPLE = _zlib_runtime_version_tuple()
 
 
-# bpo-46623: On s390x, when a hardware accelerator is used, using different
-# ways to compress data with zlib can produce different compressed data.
+# bpo-46623: When a hardware accelerator is used (currently only on s390x),
+# using different ways to compress data with zlib can produce different
+# compressed data.
 # Simplified test_pair() code:
 #
 #   def func1(data):
@@ -58,8 +59,10 @@ ZLIB_RUNTIME_VERSION_TUPLE = _zlib_runtime_version_tuple()
 #
 #   zlib.decompress(func1(data)) == zlib.decompress(func2(data)) == data
 #
-# Make the assumption that s390x always has an accelerator to simplify the skip
-# condition.
+# To simplify the skip condition, make the assumption that s390x always has an
+# accelerator, and nothing else has it.
+HW_ACCELERATED = is_s390x
+
 
 class VersionTestCase(unittest.TestCase):
 
@@ -224,12 +227,14 @@ class CompressTestCase(BaseCompressTestCase, unittest.TestCase):
                                          bufsize=zlib.DEF_BUF_SIZE),
                          HAMLET_SCENE)
 
-    @skip_on_s390x
     def test_speech128(self):
         # compress more data
         data = HAMLET_SCENE * 128
         x = zlib.compress(data)
-        self.assertEqual(zlib.compress(bytearray(data)), x)
+        # With hardware acceleration, the compressed bytes
+        # might not be identical.
+        if not HW_ACCELERATED:
+            self.assertEqual(zlib.compress(bytearray(data)), x)
         for ob in x, bytearray(x):
             self.assertEqual(zlib.decompress(ob), data)
 
@@ -276,7 +281,6 @@ class CompressTestCase(BaseCompressTestCase, unittest.TestCase):
 
 class CompressObjectTestCase(BaseCompressTestCase, unittest.TestCase):
     # Test compression object
-    @skip_on_s390x
     def test_pair(self):
         # straightforward compress/decompress objects
         datasrc = HAMLET_SCENE * 128
@@ -287,7 +291,10 @@ class CompressObjectTestCase(BaseCompressTestCase, unittest.TestCase):
             x1 = co.compress(data)
             x2 = co.flush()
             self.assertRaises(zlib.error, co.flush) # second flush should not work
-            self.assertEqual(x1 + x2, datazip)
+            # With hardware acceleration, the compressed bytes might not
+            # be identical.
+            if not HW_ACCELERATED:
+                self.assertEqual(x1 + x2, datazip)
         for v1, v2 in ((x1, x2), (bytearray(x1), bytearray(x2))):
             dco = zlib.decompressobj()
             y1 = dco.decompress(v1 + v2)
diff --git a/Misc/NEWS.d/next/Tests/2024-10-07-14-13-38.gh-issue-125041.PKLWDf.rst b/Misc/NEWS.d/next/Tests/2024-10-07-14-13-38.gh-issue-125041.PKLWDf.rst
new file mode 100644
index 00000000000..c7181eb9c1f
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2024-10-07-14-13-38.gh-issue-125041.PKLWDf.rst
@@ -0,0 +1,3 @@
+Re-enable skipped tests for :mod:`zlib` on the s390x architecture: only skip
+checks of the compressed bytes, which can be different between zlib's
+software implementation and the hardware-accelerated implementation.