Performance of overlay networks is dependent on last-mile connections, since they require that data traverse these last-mile bottlenecks at each forwarding step. This requires several times more upstream bandwidth than downstream, further exaggerating the asymmetry between down-stream and upstream bandwidth in last-mile technologies. This imbalance can cause packet queuing at the outgoing network interface of forwarding nodes, increasing latency and causing packet losses. We describe a model of a last-mile constrained overlay network and formulate and use it to solve a simplified latency- and bandwidth-bounded overlay construction problem. We observe that queueing delay may be a significant component of the end-to-end delay and approaches ignoring this may potentially result in an overlay network violating the delay and/or loss bounds. We observe that allowing a small amount of loss, it is possible to support a significantly large number of nodes. For a given end to end delay and loss bound we identify feasible degree (fan out) of each nodes. Our study sheds insights which provide engineering guidelines for designing overlays accounting for last mile problem in the Internet.