diff --git a/src/textual/_callback.py b/src/textual/_callback.py
index d2fd2403c2..6cf94daefc 100644
--- a/src/textual/_callback.py
+++ b/src/textual/_callback.py
@@ -1,7 +1,7 @@
 from __future__ import annotations
 
 import asyncio
-from functools import lru_cache, partial
+from functools import partial
 from inspect import isawaitable, signature
 from typing import TYPE_CHECKING, Any, Callable
 
@@ -16,16 +16,25 @@
 
 def count_parameters(func: Callable) -> int:
     """Count the number of parameters in a callable"""
-    if isinstance(func, partial):
-        return _count_parameters(func.func) + len(func.args)
-    if hasattr(func, "__self__"):
-        # Bound method
-        func = func.__func__  # type: ignore
-        return _count_parameters(func) - 1
-    return _count_parameters(func)
+    from ._profile import timer
+
+    with timer("count"):
+        try:
+            return func._param_count
+        except AttributeError:
+            pass
+        if isinstance(func, partial):
+            param_count = _count_parameters(func) + len(func.args)
+        elif hasattr(func, "__self__"):
+            # Bound method
+            func = func.__func__  # type: ignore
+            param_count = _count_parameters(func) - 1
+        else:
+            param_count = _count_parameters(func)
+        func._param_count = param_count
+        return param_count
 
 
-@lru_cache(maxsize=2048)
 def _count_parameters(func: Callable) -> int:
     """Count the number of parameters in a callable"""
     return len(signature(func).parameters)
diff --git a/src/textual/app.py b/src/textual/app.py
index b721507249..0f4dade599 100644
--- a/src/textual/app.py
+++ b/src/textual/app.py
@@ -1784,7 +1784,8 @@ async def run_auto_pilot(
                     await asyncio.shield(app._shutdown())
                 except asyncio.CancelledError:
                     pass
-
+        active_app.set(None)
+        active_message_pump.set(None)
         return app.return_value
 
     def run(
@@ -3029,6 +3030,8 @@ async def _close_all(self) -> None:
                 if stack_screen._running:
                     await self._prune(stack_screen)
             stack.clear()
+        self._installed_screens.clear()
+        self._modes.clear()
 
         # Close any remaining nodes
         # Should be empty by now
diff --git a/src/textual/widget.py b/src/textual/widget.py
index b71cc971ae..8b3998eb67 100644
--- a/src/textual/widget.py
+++ b/src/textual/widget.py
@@ -3676,6 +3676,7 @@ async def _message_loop_exit(self) -> None:
         parent._nodes._remove(self)
         self.app._registry.discard(self)
         self._detach()
+        self._arrangement_cache.clear()
 
     async def _on_idle(self, event: events.Idle) -> None:
         """Called when there are no more events on the queue.