In this paper we present a multicast protocol for building and maintaining Delay-Constrained Multicast Shared Trees (DCMST). Our protocol is based on the search of available Delay-Constrained multipath to graft a new receiver to the shared tree. The new receiver chooses the most promising route regarding to its available bandwidth. This way we help the equilibration of charge on the network and we offer better routes for resource reservation. In dynamic source groups the DCMST may need to be frequently updated to satisfy the delay constraint, our protocol incorporates a least cost updating mechanism. The proposed protocol scales well due to the reduced search phase which is limited to only available links.