Overriding named routes provided by Rails 3 Engines

I am working on a Ruby on Rails 3(.0) application that uses a Rails engine. However, in my local application, I want to override one of the routes provided by the Rails engine.

From the engine config/routes.rb:

match 'their_named_route' => 'controller#action', :as => 'the_route'

From my application config/routes.rb:

match 'my_named_route' => 'controller#action', :as => 'the_route'

However, when I inspect the routes, both seem to be active (and their route appears to "win", at least within the engine controllers)

$ rake routes
the_route  /my_named_route(.:format)    {:controller=>"controller", :action=>"action"}
the_route  /their_named_route(.:format) {:controller=>"controller", :action=>"action"}

Is there a good way to force my local application's named route to take priority?