A method for granular policing includes a novel policing architecture which evaluates an arriving cell's conformance by comparing the actual arrival characteristic against a family or a set of expected arrival curves. In embodiments of the present invention, expected arrival characteristics based on a connection service level agreement (SLA) are represented by a family of N arrival curves. The degree of non-conformance of a cell is evaluated by inspecting, which m arrival curves were violated and which N-m arrival curves were non-violated by the arriving cells. Subsequently in context of discard, non-conforming tagged cells are further prioritized based on their degree of non-conformance. Thus cells associated with a higher degree of non-conformance shall be discarded before cells with a relatively lower degree of non-conformance.