Replacement policies for general caching applications and Web caching in particular have been discussed extensively in the literature. Many ad-hoc policies have been proposed that attempt to take adavantage of the retrieval latency of documents, their size, the popularity of references and temporal locality of requested documents. However, the problem of finding optimal replacement policies under these factors has not been pursued in any systematic manner. In this paper, we take a step in that direction: we first show, still under the independent reference model, that a simple Markov stationary replacement policy, called the policy C*/sub 0/, minimizes the long-run average metric induced by nonuniform document costs when document eviction is optional. We then propose a framework for operating caching systems with multiple performance metrics. We do so by solving a constrained caching problem with a single constraint. The resulting constrained optimal replacement policy is obtained by simple randomization between two Markov stationary optimal replacement policies C*/sub 0/ but induced by different costs.