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We believe that a congestion control algorithm should make flows finish quickly - as quickly as possible, while staying stable and fair among flows. Recently, we proposed RCP (Rate Control Protocol) which enables typical Internet-sized flows to complete one to two orders of magnitude faster than the existing (TCP Reno) and the proposed (XCP) congestion control algorithm. Like XCP, RCP uses explicit feedback from routers, but doesn't require per-packet calculations. A router maintains just one rate that it gives to all flows, making it simple and inherently fair. Flows finish quickly because RCP aggressively gives excess bandwidth to flows, making it work well in the common case. However - and this is a design tradeoff - RCP will experience short-term transient overflows when network conditions change quickly (e.g. a route change or flash crowds). In this paper we extend RCP and propose RCP-AC (Rate Control Protocol with Acceleration Control) that allows the aggressiveness of RCP to be tuned, enabling fast completion of flows over a broad set of operating conditions.