The point-to-multipoint ABR service within ATM is important for many emerging data applications. The objective is for the source to operate at a rate representing its max-min fair share over the bottleneck link in the mul-ticast tree over which the connection is established. Resource Management (RM) cells are used by receivers to convey back to the source an explicit rate indicating their bandwidth fair share on the bottleneck of the path leading to them. Switches in the multicast tree consolidate the information in backward RM cells received from downstream switches or receivers and forward this consolidated information to their upstream switch. Most proposed consolidation algorithms attempt to maximize either the speed of the return of feedback information to the source or the accuracy of the feedback. In this paper we rst present a probabilistic consolidation algorithm that can be tuned using probability parameters to span the speed-accuracy spectrum. We then describe a technique that can be used to increase the accuracy of a broad class of switch algorithms. We demonstrate the performance of our proposed algorithms through a set of numerical examples.