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This paper deals with the creation of multicast trees in a differentiated services (DiffServ) domain. Initially, we model the integration problems of multicast & DiffServ and give a general description of our framework for multicast provisioning in DiffServ domains. Within this framework, we introduce a novel heuristic algorithm which calculates the multicast trees efficiently. The multicast tree's format and the bandwidth constraints per service class are modeled. The heuristic is based on the Dijkstra's shortest path algorithm and aims to produce the cheapest possible trees (Steiner tree problem) that conform to the defined model. The produced trees can be considered as DiffServ-customized Steiner trees. Furthermore, we evaluate the algorithm with theoretical and experimental analysis and finally, we present our conclusions.