diff --git a/Lib/test/seq_tests.py b/Lib/test/seq_tests.py
index a41970d8f3f55a..719c9434a16820 100644
--- a/Lib/test/seq_tests.py
+++ b/Lib/test/seq_tests.py
@@ -426,6 +426,7 @@ def test_pickle(self):
             self.assertEqual(lst2, lst)
             self.assertNotEqual(id(lst2), id(lst))
 
+    @support.suppress_immortalization()
     def test_free_after_iterating(self):
         support.check_free_after_iterating(self, iter, self.type2test)
         support.check_free_after_iterating(self, reversed, self.type2test)
diff --git a/Lib/test/test_capi/test_misc.py b/Lib/test/test_capi/test_misc.py
index 020e8493e57c0c..ed42d7b64302f9 100644
--- a/Lib/test/test_capi/test_misc.py
+++ b/Lib/test/test_capi/test_misc.py
@@ -26,7 +26,8 @@
 from test.support import threading_helper
 from test.support import warnings_helper
 from test.support import requires_limited_api
-from test.support import requires_gil_enabled, expected_failure_if_gil_disabled
+from test.support import suppress_immortalization
+from test.support import expected_failure_if_gil_disabled
 from test.support import Py_GIL_DISABLED
 from test.support.script_helper import assert_python_failure, assert_python_ok, run_python_until_end
 try:
@@ -481,6 +482,7 @@ def test_heap_ctype_doc_and_text_signature(self):
     def test_null_type_doc(self):
         self.assertEqual(_testcapi.NullTpDocType.__doc__, None)
 
+    @suppress_immortalization()
     def test_subclass_of_heap_gc_ctype_with_tpdealloc_decrefs_once(self):
         class HeapGcCTypeSubclass(_testcapi.HeapGcCType):
             def __init__(self):
@@ -498,6 +500,7 @@ def __init__(self):
         del subclass_instance
         self.assertEqual(type_refcnt - 1, sys.getrefcount(HeapGcCTypeSubclass))
 
+    @suppress_immortalization()
     def test_subclass_of_heap_gc_ctype_with_del_modifying_dunder_class_only_decrefs_once(self):
         class A(_testcapi.HeapGcCType):
             def __init__(self):
diff --git a/Lib/test/test_descr.py b/Lib/test/test_descr.py
index 18144c8cbb2f0a..c3f292467a6738 100644
--- a/Lib/test/test_descr.py
+++ b/Lib/test/test_descr.py
@@ -5014,6 +5014,7 @@ def __new__(cls):
                 cls.lst = [2**i for i in range(10000)]
         X.descr
 
+    @support.suppress_immortalization()
     def test_remove_subclass(self):
         # bpo-46417: when the last subclass of a type is deleted,
         # remove_subclass() clears the internal dictionary of subclasses:
diff --git a/Lib/test/test_gc.py b/Lib/test/test_gc.py
index 52681dc18cfb86..906f9884d6792f 100644
--- a/Lib/test/test_gc.py
+++ b/Lib/test/test_gc.py
@@ -3,7 +3,8 @@
 from test import support
 from test.support import (verbose, refcount_test,
                           cpython_only, requires_subprocess,
-                          requires_gil_enabled)
+                          requires_gil_enabled, suppress_immortalization,
+                          Py_GIL_DISABLED)
 from test.support.import_helper import import_module
 from test.support.os_helper import temp_dir, TESTFN, unlink
 from test.support.script_helper import assert_python_ok, make_script
@@ -109,6 +110,7 @@ def test_tuple(self):
         del l
         self.assertEqual(gc.collect(), 2)
 
+    @suppress_immortalization()
     def test_class(self):
         class A:
             pass
@@ -117,6 +119,7 @@ class A:
         del A
         self.assertNotEqual(gc.collect(), 0)
 
+    @suppress_immortalization()
     def test_newstyleclass(self):
         class A(object):
             pass
@@ -133,6 +136,7 @@ class A:
         del a
         self.assertNotEqual(gc.collect(), 0)
 
+    @suppress_immortalization()
     def test_newinstance(self):
         class A(object):
             pass
@@ -219,6 +223,7 @@ class B(object):
             self.fail("didn't find obj in garbage (finalizer)")
         gc.garbage.remove(obj)
 
+    @suppress_immortalization()
     def test_function(self):
         # Tricky: f -> d -> f, code should call d.clear() after the exec to
         # break the cycle.
@@ -561,6 +566,7 @@ def test_get_referents(self):
 
         self.assertEqual(gc.get_referents(1, 'a', 4j), [])
 
+    @suppress_immortalization()
     def test_is_tracked(self):
         # Atomic built-in types are not tracked, user-defined objects and
         # mutable containers are.
@@ -598,7 +604,9 @@ class UserFloatSlots(float):
         class UserIntSlots(int):
             __slots__ = ()
 
-        self.assertTrue(gc.is_tracked(gc))
+        if not Py_GIL_DISABLED:
+            # gh-117783: modules may be immortalized in free-threaded build
+            self.assertTrue(gc.is_tracked(gc))
         self.assertTrue(gc.is_tracked(UserClass))
         self.assertTrue(gc.is_tracked(UserClass()))
         self.assertTrue(gc.is_tracked(UserInt()))
@@ -1347,6 +1355,10 @@ def callback(ignored):
         junk = []
         i = 0
         detector = GC_Detector()
+        if Py_GIL_DISABLED:
+            # The free-threaded build doesn't have multiple generations, so
+            # just trigger a GC manually.
+            gc.collect()
         while not detector.gc_happened:
             i += 1
             if i > 10000:
@@ -1415,6 +1427,10 @@ def __del__(self):
         detector = GC_Detector()
         junk = []
         i = 0
+        if Py_GIL_DISABLED:
+            # The free-threaded build doesn't have multiple generations, so
+            # just trigger a GC manually.
+            gc.collect()
         while not detector.gc_happened:
             i += 1
             if i > 10000:
diff --git a/Lib/test/test_inspect/test_inspect.py b/Lib/test/test_inspect/test_inspect.py
index 82e466e978624f..8bd13033490b81 100644
--- a/Lib/test/test_inspect/test_inspect.py
+++ b/Lib/test/test_inspect/test_inspect.py
@@ -34,7 +34,7 @@
 except ImportError:
     ThreadPoolExecutor = None
 
-from test.support import cpython_only, import_helper
+from test.support import cpython_only, import_helper, suppress_immortalization
 from test.support import MISSING_C_DOCSTRINGS, ALWAYS_EQ
 from test.support.import_helper import DirsOnSysPath, ready_to_import
 from test.support.os_helper import TESTFN, temp_cwd
@@ -768,6 +768,7 @@ def test_getfile_builtin_function_or_method(self):
             inspect.getfile(list.append)
         self.assertIn('expected, got', str(e_append.exception))
 
+    @suppress_immortalization()
     def test_getfile_class_without_module(self):
         class CM(type):
             @property
@@ -2430,6 +2431,7 @@ def __getattribute__(self, attr):
 
         self.assertFalse(test.called)
 
+    @suppress_immortalization()
     def test_cache_does_not_cause_classes_to_persist(self):
         # regression test for gh-118013:
         # check that the internal _shadowed_dict cache does not cause
diff --git a/Lib/test/test_module/__init__.py b/Lib/test/test_module/__init__.py
index 98d1cbe824df12..952ba43f72504d 100644
--- a/Lib/test/test_module/__init__.py
+++ b/Lib/test/test_module/__init__.py
@@ -4,6 +4,7 @@
 import weakref
 from test.support import gc_collect
 from test.support import import_helper
+from test.support import suppress_immortalization
 from test.support.script_helper import assert_python_ok
 
 import sys
@@ -103,6 +104,7 @@ def f():
         gc_collect()
         self.assertEqual(f().__dict__["bar"], 4)
 
+    @suppress_immortalization()
     def test_clear_dict_in_ref_cycle(self):
         destroyed = []
         m = ModuleType("foo")
@@ -118,6 +120,7 @@ def __del__(self):
         gc_collect()
         self.assertEqual(destroyed, [1])
 
+    @suppress_immortalization()
     def test_weakref(self):
         m = ModuleType("foo")
         wr = weakref.ref(m)
diff --git a/Lib/test/test_trace.py b/Lib/test/test_trace.py
index 93966ee31d0a01..7ff3fe4091dfa4 100644
--- a/Lib/test/test_trace.py
+++ b/Lib/test/test_trace.py
@@ -1,7 +1,7 @@
 import os
 from pickle import dump
 import sys
-from test.support import captured_stdout, requires_resource
+from test.support import captured_stdout, requires_resource, requires_gil_enabled
 from test.support.os_helper import (TESTFN, rmtree, unlink)
 from test.support.script_helper import assert_python_ok, assert_python_failure
 import textwrap
@@ -301,6 +301,7 @@ def test_loop_caller_importing(self):
 
     @unittest.skipIf(hasattr(sys, 'gettrace') and sys.gettrace(),
                      'pre-existing trace function throws off measurements')
+    @requires_gil_enabled("gh-117783: immortalization of types affects traced method names")
     def test_inst_method_calling(self):
         obj = TracedClass(20)
         self.tracer.runfunc(obj.inst_method_calling, 1)
@@ -334,6 +335,7 @@ def setUp(self):
 
     @unittest.skipIf(hasattr(sys, 'gettrace') and sys.gettrace(),
                      'pre-existing trace function throws off measurements')
+    @requires_gil_enabled("gh-117783: immortalization of types affects traced method names")
     def test_loop_caller_importing(self):
         self.tracer.runfunc(traced_func_importing_caller, 1)
 
diff --git a/Lib/test/test_zoneinfo/test_zoneinfo.py b/Lib/test/test_zoneinfo/test_zoneinfo.py
index 8414721555731e..8bcd6d2e9951b9 100644
--- a/Lib/test/test_zoneinfo/test_zoneinfo.py
+++ b/Lib/test/test_zoneinfo/test_zoneinfo.py
@@ -17,7 +17,7 @@
 from datetime import date, datetime, time, timedelta, timezone
 from functools import cached_property
 
-from test.support import MISSING_C_DOCSTRINGS
+from test.support import MISSING_C_DOCSTRINGS, requires_gil_enabled
 from test.test_zoneinfo import _support as test_support
 from test.test_zoneinfo._support import OS_ENV_LOCK, TZPATH_TEST_LOCK, ZoneInfoTestBase
 from test.support.import_helper import import_module, CleanImport
@@ -1931,6 +1931,7 @@ def test_cache_location(self):
         self.assertFalse(hasattr(c_zoneinfo.ZoneInfo, "_weak_cache"))
         self.assertTrue(hasattr(py_zoneinfo.ZoneInfo, "_weak_cache"))
 
+    @requires_gil_enabled("gh-117783: types may be immortalized")
     def test_gc_tracked(self):
         import gc