diff --git a/Lib/test/test_inspect/test_inspect.py b/Lib/test/test_inspect/test_inspect.py
index 2c950e46b3e..d536d04d2e7 100644
--- a/Lib/test/test_inspect/test_inspect.py
+++ b/Lib/test/test_inspect/test_inspect.py
@@ -1,5 +1,4 @@
 from annotationlib import Format, ForwardRef
-import asyncio
 import builtins
 import collections
 import copy
@@ -73,11 +72,6 @@ def revise(filename, *args):
 git = mod.StupidGit()
 
 
-def tearDownModule():
-    if support.has_socket_support:
-        asyncio._set_event_loop_policy(None)
-
-
 def signatures_with_lexicographic_keyword_only_parameters():
     """
     Yields a whole bunch of functions with only keyword-only parameters,
@@ -205,7 +199,7 @@ def test_excluding_predicates(self):
         self.assertFalse(inspect.ismethodwrapper(type("AnyClass", (), {})))
 
     def test_ispackage(self):
-        self.istest(inspect.ispackage, 'asyncio')
+        self.istest(inspect.ispackage, 'unittest')
         self.istest(inspect.ispackage, 'importlib')
         self.assertFalse(inspect.ispackage(inspect))
         self.assertFalse(inspect.ispackage(mod))
@@ -1166,16 +1160,20 @@ def f(self):
                 # This is necessary when the test is run multiple times.
                 sys.modules.pop("inspect_actual")
 
-    @unittest.skipIf(
-        support.is_emscripten or support.is_wasi,
-        "socket.accept is broken"
-    )
     def test_nested_class_definition_inside_async_function(self):
-        import asyncio
-        self.addCleanup(asyncio.set_event_loop_policy, None)
-        self.assertSourceEqual(asyncio.run(mod2.func225()), 226, 227)
+        def run(coro):
+            try:
+                coro.send(None)
+            except StopIteration as e:
+                return e.value
+            else:
+                raise RuntimeError("coroutine did not complete synchronously!")
+            finally:
+                coro.close()
+
+        self.assertSourceEqual(run(mod2.func225()), 226, 227)
         self.assertSourceEqual(mod2.cls226, 231, 235)
-        self.assertSourceEqual(asyncio.run(mod2.cls226().func232()), 233, 234)
+        self.assertSourceEqual(run(mod2.cls226().func232()), 233, 234)
 
     def test_class_definition_same_name_diff_methods(self):
         self.assertSourceEqual(mod2.cls296, 296, 298)