diff --git a/Lib/contextlib.py b/Lib/contextlib.py
index 95947aceccc..f82e7bca357 100644
--- a/Lib/contextlib.py
+++ b/Lib/contextlib.py
@@ -557,11 +557,12 @@ class ExitStack(_BaseExitStack, AbstractContextManager):
         return self
 
     def __exit__(self, *exc_details):
-        received_exc = exc_details[0] is not None
+        exc = exc_details[1]
+        received_exc = exc is not None
 
         # We manipulate the exception state so it behaves as though
         # we were actually nesting multiple with statements
-        frame_exc = sys.exc_info()[1]
+        frame_exc = sys.exception()
         def _fix_exception_context(new_exc, old_exc):
             # Context may not be correct, so find the end of the chain
             while 1:
@@ -584,24 +585,28 @@ class ExitStack(_BaseExitStack, AbstractContextManager):
             is_sync, cb = self._exit_callbacks.pop()
             assert is_sync
             try:
+                if exc is None:
+                    exc_details = None, None, None
+                else:
+                    exc_details = type(exc), exc, exc.__traceback__
                 if cb(*exc_details):
                     suppressed_exc = True
                     pending_raise = False
-                    exc_details = (None, None, None)
-            except:
-                new_exc_details = sys.exc_info()
+                    exc = None
+            except BaseException as new_exc:
                 # simulate the stack of exceptions by setting the context
-                _fix_exception_context(new_exc_details[1], exc_details[1])
+                _fix_exception_context(new_exc, exc)
                 pending_raise = True
-                exc_details = new_exc_details
+                exc = new_exc
+
         if pending_raise:
             try:
-                # bare "raise exc_details[1]" replaces our carefully
+                # bare "raise exc" replaces our carefully
                 # set-up context
-                fixed_ctx = exc_details[1].__context__
-                raise exc_details[1]
+                fixed_ctx = exc.__context__
+                raise exc
             except BaseException:
-                exc_details[1].__context__ = fixed_ctx
+                exc.__context__ = fixed_ctx
                 raise
         return received_exc and suppressed_exc
 
@@ -697,11 +702,12 @@ class AsyncExitStack(_BaseExitStack, AbstractAsyncContextManager):
         return self
 
     async def __aexit__(self, *exc_details):
-        received_exc = exc_details[0] is not None
+        exc = exc_details[1]
+        received_exc = exc is not None
 
         # We manipulate the exception state so it behaves as though
         # we were actually nesting multiple with statements
-        frame_exc = sys.exc_info()[1]
+        frame_exc = sys.exception()
         def _fix_exception_context(new_exc, old_exc):
             # Context may not be correct, so find the end of the chain
             while 1:
@@ -723,6 +729,10 @@ class AsyncExitStack(_BaseExitStack, AbstractAsyncContextManager):
         while self._exit_callbacks:
             is_sync, cb = self._exit_callbacks.pop()
             try:
+                if exc is None:
+                    exc_details = None, None, None
+                else:
+                    exc_details = type(exc), exc, exc.__traceback__
                 if is_sync:
                     cb_suppress = cb(*exc_details)
                 else:
@@ -731,21 +741,21 @@ class AsyncExitStack(_BaseExitStack, AbstractAsyncContextManager):
                 if cb_suppress:
                     suppressed_exc = True
                     pending_raise = False
-                    exc_details = (None, None, None)
-            except:
-                new_exc_details = sys.exc_info()
+                    exc = None
+            except BaseException as new_exc:
                 # simulate the stack of exceptions by setting the context
-                _fix_exception_context(new_exc_details[1], exc_details[1])
+                _fix_exception_context(new_exc, exc)
                 pending_raise = True
-                exc_details = new_exc_details
+                exc = new_exc
+
         if pending_raise:
             try:
-                # bare "raise exc_details[1]" replaces our carefully
+                # bare "raise exc" replaces our carefully
                 # set-up context
-                fixed_ctx = exc_details[1].__context__
-                raise exc_details[1]
+                fixed_ctx = exc.__context__
+                raise exc
             except BaseException:
-                exc_details[1].__context__ = fixed_ctx
+                exc.__context__ = fixed_ctx
                 raise
         return received_exc and suppressed_exc
 
diff --git a/Lib/test/test_contextlib.py b/Lib/test/test_contextlib.py
index ecc5a43dad4..dbc7dfcc24b 100644
--- a/Lib/test/test_contextlib.py
+++ b/Lib/test/test_contextlib.py
@@ -1085,7 +1085,7 @@ class TestBaseExitStack:
 class TestExitStack(TestBaseExitStack, unittest.TestCase):
     exit_stack = ExitStack
     callback_error_internal_frames = [
-        ('__exit__', 'raise exc_details[1]'),
+        ('__exit__', 'raise exc'),
         ('__exit__', 'if cb(*exc_details):'),
     ]
 
diff --git a/Lib/test/test_contextlib_async.py b/Lib/test/test_contextlib_async.py
index bb72ae74e58..fa89c23f8ed 100644
--- a/Lib/test/test_contextlib_async.py
+++ b/Lib/test/test_contextlib_async.py
@@ -557,7 +557,7 @@ class TestAsyncExitStack(TestBaseExitStack, unittest.TestCase):
         ('__exit__', 'return self.run_coroutine(self.__aexit__(*exc_details))'),
         ('run_coroutine', 'raise exc'),
         ('run_coroutine', 'raise exc'),
-        ('__aexit__', 'raise exc_details[1]'),
+        ('__aexit__', 'raise exc'),
         ('__aexit__', 'cb_suppress = cb(*exc_details)'),
     ]