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Current TCP-friendly congestion control mechanisms such as those used in TFRC adjust the packet rate in order to adapt to network conditions and obtain a throughput not exceeding that of a TCP connection operating under the same conditions. In an environment where the bottleneck resource is packet processing, this is the correct behavior. However, if the bottleneck resource is bandwidth, and flows may use packets of different sizes, resource sharing then depends on packet size and is no longer fair. Now for some applications, such as Internet telephony, it is more natural to adjust the packet size, while keeping the packet rate as constant as possible. In this paper we study the impact of variations in packet size on equation-based congestion control and propose methods to remove the throughput bias resulting from the use of different packet sizes. We investigate in detail the design space of the approaches by means of mathematical analysis and propose a number of possible designs. We evaluate these designs through simulation and conclude with some concrete proposals. Our findings can be used to design a TCP-friendly congestion control mechanism for applications that adjust packet size rather than rate, or that are forced to use a small packet size. We base our analysis on the TFRC protocol, but similar considerations also hold for other congestion control mechanisms.