Traceroute is a networking tool that allows one to discover the path that packets take from a source machine, through the network, to a destination machine. It is widely used as an engineering tool, and also as a scientific tool, such as for discovery of the network topology at the IP level. In prior work, authors on this technical report have shown how to improve the efficiency of route tracing from multiple cooperating monitors. However , it is not unusual for a route tracing monitor to operate in isolation. Somewhat different strategies are required for this case, and this report is the first systematic study of those requirements. Standard traceroute is inefficient when used repeatedly towards multiple destinations , as it repeatedly probes the same interfaces close to the source. Others have recognized this inefficiency and have proposed tracing backwards from the destinations and stopping probing upon encounter with a previously-seen interface. One of this technical report's contributions is to quantify for the first time the efficiency of this approach. Another contribution is to describe the effect of non-responding destinations on this efficiency. Since a large portion of destination machines do not reply to probe packets, backwards probing from the destination is often infeasible. We propose an algorithm to tackle non-responding destinations, and we find that our algorithm can strongly decrease probing redundancy at the cost of a small reduction in node and link discovery.