This paper examines replication in content distribution networks and proposes a novel mechanism for optimally resolving performance versus cost tradeoffs. The key insight behind our work is to formally and analytically capture the relationship between performance, bandwidth overhead and storage requirements for a web cache, express the system goals as a mathematical optimization problem, and solve for the optimal extent of replication that achieves the desired system goals with minimal overhead. We describe the design and implementation of a new content distribution network based on this concept, called CobWeb. CobWeb can achieve a target lookup latency while minimizing network and storage overhead, minimize access time while keeping bandwidth usage below a set limit, and alleviate "flash crowd" effects by rapidly replicating popular objects through fast and highly adaptive replica management. We outline the architecture of the CobWeb system, describe its novel optimization algorithm for intelligent resource allocation, and compare, through simulations and a physical deployment on PlanetLab, CobWeb's informed, analysis-driven replication strategy to existing approaches based on passive caching and heuristics.