Internet routers today can be overwhelmed by a large number of BGP updates triggered by events such as session resets, link failures, and policy changes. Such excessive updates can delay routing convergence, which, in turn, degrades the performance of delay-and jitter-sensitive applications. This paper proposes a simple and novel idea of differentiated processing of BGP updates to reduce routers' load and improve routing convergence without changing the protocol semantics. Based on a set of criteria, BGP updates are grouped into different priority classes. Higher-priority updates are processed and propagated sooner, while lower-priority ones, not affecting routing decisions, can be delayed to both reduce routers' load and improve routing convergence. We first present a general methodology for update classification, update processing, and priority-state inference. By analyzing real BGP data obtained from Route Views, we show that our update classification is feasible and beneficial. We further propose two differentiated update processing (DUP) algorithms and evaluate them using the SSFNet BGP simulator on several realistic network topologies. The algorithms are shown to be very effective for large networks, yielding 30% fewer updates and reducing convergence time by 80%. Our scheme is simple and light-weight with little added processing overhead. It can be deployed incrementally, since BGP messages are not modified and every BGP router makes routing decisions independently.