The present invention concerns a technique for providing Class-of-Service Routing in an ATM network (10) that utilizes the Private Network-Network Interface (PNNI) protocol. An originating node seeking to route a call to a terminating node does so by initially determining the class-of-service and then selecting a shortest length path there-between. Each successive link on the selected path is examined for sufficient available bandwidth and available depth (i.e., bandwidth not reserved for other services) for the Class-of-Service of the call. If every link possesses sufficient available bandwidth, then the call passes on the selected path. Otherwise, should a link on the selected path lack sufficient bandwidth and available depth, then a crankback message is sent to the originating node, and the originating node selects the next shortest path. Thereafter, the process of examining each link for sufficient bandwidth is repeated. If no path is found, the call is ultimately blocked.