A recent means for enabling multicast in the Internet involves deploying network overlays where end-systems participate in the forwarding of data to other end-systems. The use of overlays not only permits individual sessions to simultaneously structure their communication trees atop unicast-only networks, but also gives the session greater flexibility when forming the topology of the forwarding tree. Even though multiple sessions are often expected to compete for the same network overlay resources, most work to date assumes that overlay protocols operate as though each session has isolated access to the available overlay resources. We consider two algorithms that build depth-bounded overlay trees where each node's outgoing bandwidth constrains the number of nodes to which it can directly forward data. One algorithm tries to cluster a node's available bandwidth within a single tree, the other tries to disperse the available bandwidth among multiple trees. We prove analytically that when node capacities are identical and session requirements are identical that a clustering approach will increase the number of sessions that can co-exist. However, simulation results reveal that in heterogeneous networking environments or in environments where session participants vary with time, the dispersing algorithm outperforms the clustering algorithm. These results can be used to guide future development of overlay protocols that must partition resources among multiple sessions.