The use of end-to-end multicast traffic measurements has been recently proposed as a means to infer network internal characteristics as packet link loss rate and delay. In this paper, we propose an algorithm that infers the multicast tree topology based on these end-to-end measurements. Differently from previous approaches which make only partial use of the available information, this algorithm adaptively combines different performance measures to reconstruct the topology. We establish its consistency and evaluate its accuracy through simulation. We show that in general it requires many fewer probes to correctly identify the topology than other methods.