diff --git a/Lib/test/test_logging.py b/Lib/test/test_logging.py
index 3f0b363066df2c..871c751dc21289 100644
--- a/Lib/test/test_logging.py
+++ b/Lib/test/test_logging.py
@@ -4569,27 +4569,25 @@ def test_msecs_has_no_floating_point_precision_loss(self):
             self.assertEqual(record.msecs, want)
             self.assertEqual(record.created, ns / 1e9)
 
+    # The test overrides a private attribute
+    @support.cpython_only
     def test_relativeCreated_has_higher_precision(self):
         # See issue gh-102402
         ns = 1_677_903_920_000_998_503  # approx. 2023-03-04 04:25:20 UTC
         offsets_ns = (200, 500, 12_354, 99_999, 1_677_903_456_999_123_456)
-        orig_modules = import_helper._save_and_remove_modules(['logging'])
-        try:
-            with patch("time.time_ns") as patched_ns:
-                # mock for module import
-                patched_ns.return_value = ns
-                import logging
-                for offset_ns in offsets_ns:
-                    new_ns = ns + offset_ns
-                    # mock for log record creation
-                    patched_ns.return_value = new_ns
-                    record = logging.makeLogRecord({'msg': 'test'})
-                    self.assertAlmostEqual(record.created, new_ns / 1e9, places=6)
-                    # After PR gh-102412, precision (places) increases from 3 to 7
-                    self.assertAlmostEqual(record.relativeCreated, offset_ns / 1e6, places=7)
-        finally:
-            import_helper._save_and_remove_modules(['logging'])
-            sys.modules.update(orig_modules)
+
+        with (patch("time.time_ns") as time_ns_mock,
+              support.swap_attr(logging, '_startTime', ns)):
+            for offset_ns in offsets_ns:
+                # mock for log record creation
+                new_ns = ns + offset_ns
+                time_ns_mock.return_value = new_ns
+
+                record = logging.makeLogRecord({'msg': 'test'})
+                self.assertAlmostEqual(record.created, new_ns / 1e9, places=6)
+
+                # After PR gh-102412, precision (places) increases from 3 to 7
+                self.assertAlmostEqual(record.relativeCreated, offset_ns / 1e6, places=7)
 
 
 class TestBufferingFormatter(logging.BufferingFormatter):