A dispensing closure system is provided for a container that has an opening to the container interior. The preferred embodiment of the system includes a closure having a closure body for extending from the container at the container opening and a lid hingedly attached to the closure body. The closure body has a dispensing spout, and the lid includes a hollow spud for entering the spout. A spud rim can be provided on the spud, extending inwardly towards the hollow interior of the spud. A lid rim can additionally or alternatively be provided on the inside surface of the lid, positioned within the hollow interior of the spud.