diff --git a/Lib/test/test_import/__init__.py b/Lib/test/test_import/__init__.py
index 11eaae5e47e..b09065f812c 100644
--- a/Lib/test/test_import/__init__.py
+++ b/Lib/test/test_import/__init__.py
@@ -2887,12 +2887,15 @@ class SinglephaseInitTests(unittest.TestCase):
 
                 self.assertIs(reloaded.snapshot.cached, reloaded.module)
 
+    @unittest.skipIf(_testinternalcapi is None, "requires _testinternalcapi")
     def test_check_state_first(self):
         for variant in ['', '_with_reinit', '_with_state']:
             name = f'{self.NAME}{variant}_check_cache_first'
             with self.subTest(name):
                 mod = self._load_dynamic(name, self.ORIGIN)
                 self.assertEqual(mod.__name__, name)
+                sys.modules.pop(name, None)
+                _testinternalcapi.clear_extension(name, self.ORIGIN)
 
     # Currently, for every single-phrase init module loaded
     # in multiple interpreters, those interpreters share a
diff --git a/Modules/_testsinglephase.c b/Modules/_testsinglephase.c
index bcdb5ba3184..066e0dbfb63 100644
--- a/Modules/_testsinglephase.c
+++ b/Modules/_testsinglephase.c
@@ -682,6 +682,9 @@ finally:
 /* the _testsinglephase_*_check_cache_first modules */
 /****************************************************/
 
+/* Each of these modules should only be freshly loaded.  That means
+   clearing the caches and each module def's m_base after each load. */
+
 static struct PyModuleDef _testsinglephase_check_cache_first = {
     PyModuleDef_HEAD_INIT,
     .m_name = "_testsinglephase_check_cache_first",
diff --git a/Python/import.c b/Python/import.c
index 4f3325aa67b..6fe6df4db4f 100644
--- a/Python/import.c
+++ b/Python/import.c
@@ -494,7 +494,7 @@ _modules_by_index_check(PyInterpreterState *interp, Py_ssize_t index)
     if (MODULES_BY_INDEX(interp) == NULL) {
         return "Interpreters module-list not accessible.";
     }
-    if (index > PyList_GET_SIZE(MODULES_BY_INDEX(interp))) {
+    if (index >= PyList_GET_SIZE(MODULES_BY_INDEX(interp))) {
         return "Module index out of bounds.";
     }
     return NULL;
@@ -2183,7 +2183,7 @@ clear_singlephase_extension(PyInterpreterState *interp,
     /* Clear data set when the module was initially loaded. */
     def->m_base.m_init = NULL;
     Py_CLEAR(def->m_base.m_copy);
-    // We leave m_index alone since there's no reason to reset it.
+    def->m_base.m_index = 0;
 
     /* Clear the PyState_*Module() cache entry. */
     Py_ssize_t index = _get_cached_module_index(cached);