diff --git a/Lib/test/test_charmapcodec.py b/Lib/test/test_charmapcodec.py
index 0d4594d..3f62890 100644
--- a/Lib/test/test_charmapcodec.py
+++ b/Lib/test/test_charmapcodec.py
@@ -20,12 +20,15 @@
         return tuple(testcodec.getregentry())
     return None
 
-codecs.register(codec_search_function)
-
 # test codec's name (see test/testcodec.py)
 codecname = 'testcodec'
 
 class CharmapCodecTest(unittest.TestCase):
+
+    def setUp(self):
+        codecs.register(codec_search_function)
+        self.addCleanup(codecs.unregister, codec_search_function)
+
     def test_constructorx(self):
         self.assertEqual(str(b'abc', codecname), 'abc')
         self.assertEqual(str(b'xdef', codecname), 'abcdef')
diff --git a/Lib/test/test_codecs.py b/Lib/test/test_codecs.py
index 09ceef7..9be8281 100644
--- a/Lib/test/test_codecs.py
+++ b/Lib/test/test_codecs.py
@@ -2754,29 +2754,14 @@
 
 def _get_test_codec(codec_name):
     return _TEST_CODECS.get(codec_name)
-codecs.register(_get_test_codec) # Returns None, not usable as a decorator
-
-try:
-    # Issue #22166: Also need to clear the internal cache in CPython
-    from _codecs import _forget_codec
-except ImportError:
-    def _forget_codec(codec_name):
-        pass
 
 
 class ExceptionChainingTest(unittest.TestCase):
 
     def setUp(self):
-        # There's no way to unregister a codec search function, so we just
-        # ensure we render this one fairly harmless after the test
-        # case finishes by using the test case repr as the codec name
-        # The codecs module normalizes codec names, although this doesn't
-        # appear to be formally documented...
-        # We also make sure we use a truly unique id for the custom codec
-        # to avoid issues with the codec cache when running these tests
-        # multiple times (e.g. when hunting for refleaks)
-        unique_id = repr(self) + str(id(self))
-        self.codec_name = encodings.normalize_encoding(unique_id).lower()
+        self.codec_name = 'exception_chaining_test'
+        codecs.register(_get_test_codec)
+        self.addCleanup(codecs.unregister, _get_test_codec)
 
         # We store the object to raise on the instance because of a bad
         # interaction between the codec caching (which means we can't
@@ -2791,10 +2776,6 @@
         _TEST_CODECS.pop(self.codec_name, None)
         # Issue #22166: Also pop from caches to avoid appearance of ref leaks
         encodings._cache.pop(self.codec_name, None)
-        try:
-            _forget_codec(self.codec_name)
-        except KeyError:
-            pass
 
     def set_codec(self, encode, decode):
         codec_info = codecs.CodecInfo(encode, decode,
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index 85fac30..fbaea3a 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -2529,10 +2529,6 @@
                 streamreader=None, streamwriter=None,
                 incrementaldecoder=cls)
 
-# Register the previous decoder for testing.
-# Disabled by default, tests will enable it.
-codecs.register(StatefulIncrementalDecoder.lookupTestDecoder)
-
 
 class StatefulIncrementalDecoderTest(unittest.TestCase):
     """
@@ -2583,6 +2579,9 @@
         self.testdata = b"AAA\r\nBBB\rCCC\r\nDDD\nEEE\r\n"
         self.normalized = b"AAA\nBBB\nCCC\nDDD\nEEE\n".decode("ascii")
         os_helper.unlink(os_helper.TESTFN)
+        codecs.register(StatefulIncrementalDecoder.lookupTestDecoder)
+        self.addCleanup(codecs.unregister,
+                        StatefulIncrementalDecoder.lookupTestDecoder)
 
     def tearDown(self):
         os_helper.unlink(os_helper.TESTFN)
diff --git a/Lib/test/test_unicode.py b/Lib/test/test_unicode.py
index d485bc7..90b0965 100644
--- a/Lib/test/test_unicode.py
+++ b/Lib/test/test_unicode.py
@@ -36,7 +36,6 @@
         return (encode2, decode2, None, None)
     else:
         return None
-codecs.register(search_function)
 
 def duplicate_string(text):
     """
@@ -58,6 +57,10 @@
 
     type2test = str
 
+    def setUp(self):
+        codecs.register(search_function)
+        self.addCleanup(codecs.unregister, search_function)
+
     def checkequalnofix(self, result, object, methodname, *args):
         method = getattr(object, methodname)
         realresult = method(*args)