We present a new routing algorithm to compute paths within a network using dynamic link metrics. Dynamic link metrics are cost metrics that depend on a link's dynamic characteristics, e.g., the congestion on the link. Our algorithm is destination-initiated: the destination initiates a global path computation to itself using dynamic link metrics. All other destinations that do not initiate this dynamic metric computation use paths that are calculated and maintained by a traditional routing algorithm using static link metrics. Analysis of Internet packet traces show that a high percentage of network traffic is destined for a small number of networks. Because our algorithm is destination-initiated, it achieves maximum performance at minimum cost when it only recomputes dynamic metric paths to these selected "hot" destination networks. This selective approach to route recomputation reduces many of the problems (principally route oscillations) associated with calculating all routes simultaneously. We compare the routing efficiency and end-to-end performance of our algorithm against those of traditional algorithms using dynamic link metrics. The results of our experiments show that our algorithm can provide higher network performance at a significantly lower routing cost under conditions that arise in real networks. The effectiveness of the algorithm stems from the independent, time-staggered recomputation of important paths using dynamic metrics, allowing for splits in congested traffic that cannot be made by traditional routing algorithms.