diff --git a/src/textual/app.py b/src/textual/app.py
index ed22f3c54..2ada12f61 100644
--- a/src/textual/app.py
+++ b/src/textual/app.py
@@ -196,7 +196,7 @@ class App(Generic[ReturnType], DOMNode):
 
         self._logger = Logger(self._log)
 
-        self._bindings.bind("ctrl+c", "quit", show=False, allow_forward=False)
+        self._bindings.bind("ctrl+c", "quit", show=False, universal=True)
         self._refresh_required = False
 
         self.design = DEFAULT_COLORS
@@ -1282,11 +1282,12 @@ class App(Generic[ReturnType], DOMNode):
             namespace_bindings = [(node, node._bindings) for node in focused.ancestors]
         return namespace_bindings
 
-    async def check_bindings(self, key: str) -> bool:
+    async def check_bindings(self, key: str, universal: bool = False) -> bool:
         """Handle a key press.
 
         Args:
             key (str): A key
+            universal (bool): Check universal keys if True, otherwise non-universal keys.
 
         Returns:
             bool: True if the key was handled by a binding, otherwise False
@@ -1294,7 +1295,7 @@ class App(Generic[ReturnType], DOMNode):
 
         for namespace, bindings in self._binding_chain:
             binding = bindings.keys.get(key)
-            if binding is not None:
+            if binding is not None and binding.universal == universal:
                 await self.action(binding.action, default_namespace=namespace)
                 return True
         return False
@@ -1312,11 +1313,11 @@ class App(Generic[ReturnType], DOMNode):
             if isinstance(event, events.MouseEvent):
                 # Record current mouse position on App
                 self.mouse_position = Offset(event.x, event.y)
-            if isinstance(event, events.Key):
-                forward_target = self.focused or self.screen
-                await forward_target._forward_event(event)
-            else:
                 await self.screen._forward_event(event)
+            elif isinstance(event, events.Key):
+                if not await self.check_bindings(event.key, universal=True):
+                    forward_target = self.focused or self.screen
+                    await forward_target._forward_event(event)
 
         elif isinstance(event, events.Paste):
             if self.focused is not None:
diff --git a/src/textual/binding.py b/src/textual/binding.py
index 498201c76..39984f517 100644
--- a/src/textual/binding.py
+++ b/src/textual/binding.py
@@ -34,7 +34,7 @@ class Binding:
     """Show the action in Footer, or False to hide."""
     key_display: str | None = None
     """How the key should be shown in footer."""
-    allow_forward: bool = True
+    universal: bool = False
     """Allow forwarding from app to focused widget."""
 
 
@@ -55,7 +55,7 @@ class Bindings:
                                 description=binding.description,
                                 show=binding.show,
                                 key_display=binding.key_display,
-                                allow_forward=binding.allow_forward,
+                                universal=binding.universal,
                             )
                             yield new_binding
                     else:
@@ -103,7 +103,7 @@ class Bindings:
         description: str = "",
         show: bool = True,
         key_display: str | None = None,
-        allow_forward: bool = True,
+        universal: bool = False,
     ) -> None:
         all_keys = [key.strip() for key in keys.split(",")]
         for key in all_keys:
@@ -113,7 +113,7 @@ class Bindings:
                 description,
                 show=show,
                 key_display=key_display,
-                allow_forward=allow_forward,
+                universal=universal,
             )
 
     def get_key(self, key: str) -> Binding:
@@ -126,4 +126,4 @@ class Bindings:
         binding = self.keys.get(key, None)
         if binding is None:
             return True
-        return binding.allow_forward
+        return not binding.universal