The construction of multicast trees is complicated by the need to balance a number of important objectives, including: minimizing latencies, minimizing depth/hops, and bounding the degree. In this paper we study the problem of determining a degree-bounded directed spanning tree of minimum average-latency in a complete graph where the inter-node latencies determine a metric. In particular, we focus on measuring the effects on average latency when imposing depth constraints (i.e., bounds on hop count) on degree-bounded spanning trees. The general problem is a well known NP-hard problem, and several recent works have proposed approximate solutions which aim at minimizing either depth or latency. In this work, we present a new heuristic algorithm which improves upon previous solutions by considering both depth and latency and the tradeoffs between them. Our algorithms are shown to improve the theoretical worst-case approximation factors, and we show improvements under empirical evaluation. Our experiments examine and analyze several different topologies, including, low-dimensional random geometric networks, random transit-stub networks, and high-dimensional hypercube networks. We show how our solutions can be applied in the context of enabling multicasting support in locality aware peer-to-peer overlay networks.