In this paper, we develop efficient admission control tests for member join/leave (and its associated state refresh and update procedures) for receiver-initiated core-based multicast routing, e.g., Core Based Tree (CBT) Protocol, to allow construction of QoS-capable multicast trees, while making the minimum possible impact to the existing infrastructure.Specifically, we (i) derive sufficient conditions for a multicast tree to maintain its QoS; (ii) devise effective admission tests to verify whether or not a group member may join the multicast tree at adequate QoS, while not violating existing QoS guarantees to other on-tree members; and (iii) identify the minimum set of state information required for the admission tests and develop a soft state refresh and update procedure. We also investigate how to support receiver heterogeneity and accommodate both the controlled-load and guaranteed QoS network services. Finally, we validate the effectiveness of the proposed mechanism by incorporating them into the CBT protocol, and evaluate them via event-driven simulations in terms of the probability of join requests being rejected, message overhead, and scalability.