diff --git a/starlette/applications.py b/starlette/applications.py
index c95fa0a5c..b754bb967 100644
--- a/starlette/applications.py
+++ b/starlette/applications.py
@@ -8,6 +8,12 @@
 from starlette.routing import BaseRoute, Router
 from starlette.types import ASGIApp, Receive, Scope, Send
 
+_ExcKey = typing.TypeVar(
+    "_ExcKey",
+    bound=typing.Union[int, typing.Type[Exception]],
+    contravariant=True,
+)
+
 
 class Starlette:
     """
@@ -23,11 +29,10 @@ class Starlette:
     any uncaught errors occurring anywhere in the entire stack.
     `ExceptionMiddleware` is added as the very innermost middleware, to deal
     with handled exception cases occurring in the routing or endpoints.
-    * **exception_handlers** - A dictionary mapping either integer status codes,
-    or exception class types onto callables which handle the exceptions.
-    Exception handler callables should be of the form
-    `handler(request, exc) -> response` and may be be either standard functions, or
-    async functions.
+    * **exception_handlers** - A mapping of either integer status codes, or exception
+    class types onto callables which handle the exceptions. Exception handler
+    callables should be of the form `handler(request, exc) -> response` and may be
+    either standard functions, or async functions.
     * **on_startup** - A list of callables to run on application startup.
     Startup handler callables do not take any arguments, and may be be either
     standard functions, or async functions.
@@ -41,9 +46,7 @@ def __init__(
         debug: bool = False,
         routes: typing.Sequence[BaseRoute] = None,
         middleware: typing.Sequence[Middleware] = None,
-        exception_handlers: typing.Dict[
-            typing.Union[int, typing.Type[Exception]], typing.Callable
-        ] = None,
+        exception_handlers: typing.Mapping[_ExcKey, typing.Callable] = None,
         on_startup: typing.Sequence[typing.Callable] = None,
         on_shutdown: typing.Sequence[typing.Callable] = None,
         lifespan: typing.Callable[["Starlette"], typing.AsyncContextManager] = None,
@@ -59,7 +62,7 @@ def __init__(
         self.router = Router(
             routes, on_startup=on_startup, on_shutdown=on_shutdown, lifespan=lifespan
         )
-        self.exception_handlers = (
+        self.exception_handlers: typing.Dict[_ExcKey, typing.Callable] = (
             {} if exception_handlers is None else dict(exception_handlers)
         )
         self.user_middleware = [] if middleware is None else list(middleware)
@@ -128,7 +131,7 @@ def add_middleware(self, middleware_class: type, **options: typing.Any) -> None:
 
     def add_exception_handler(
         self,
-        exc_class_or_status_code: typing.Union[int, typing.Type[Exception]],
+        exc_class_or_status_code: _ExcKey,
         handler: typing.Callable,
     ) -> None:
         self.exception_handlers[exc_class_or_status_code] = handler
@@ -154,9 +157,7 @@ def add_websocket_route(
     ) -> None:
         self.router.add_websocket_route(path, route, name=name)
 
-    def exception_handler(
-        self, exc_class_or_status_code: typing.Union[int, typing.Type[Exception]]
-    ) -> typing.Callable:
+    def exception_handler(self, exc_class_or_status_code: _ExcKey) -> typing.Callable:
         def decorator(func: typing.Callable) -> typing.Callable:
             self.add_exception_handler(exc_class_or_status_code, func)
             return func