1. In a system having a processor for performing assigned tasks and an adapter for connecting the system to a network to receive incoming packets of varying size, wherein said incoming packets respectively carry interrupt messages disposed to interrupt said processor in performing said assigned tasks, a method for operating said system in response to said incoming packets comprising the steps of: determining whether or not a particular incoming packet meets one or more prespecified criteria, at least a first criterion of said prespecified criteria being related to the size of said particular incoming packet; immediately interrupting said processor in accordance with the interrupt message carried by said particular packet, if said particular packet meets all of said prespecified criteria; and interrupting said processor in accordance with a specified interrupt coalescing technique, if said incoming particular packet does not meet all of said prespecified criteria.