Emerging Internet applications create the need for advanced packet classifiers. This paper investigates the mechanisms that determine the performance of state-of-the-art multi-field classification methods, and proposes a novel scheme called P2C for packet classification at OC-192 and OC-768 speeds. P2C combines the strengths of embedded memory and ternary CAM technologies to achieve very high storage efficiency while maintaining fast incremental updates. Key feature of the new scheme Is Its ability to adapt to the complexity of a classification rule set, while providing effective control over the update dynamics and storage requirements at the granularity of individual rules. This makes P2C suitable for a broad range of applications.