We investigate the performance limitations in the case of a large number of long distance voice over IP calls originating from different sources and transported through a best-effort IP network. We focus on the potentially negative effects of total protocol header overhead, which is twice the voice payload generated by the high-compression audio codecs. These negative effects range from the inefficient use of bandwidth to the network congestion caused by the large number of short voice packets flowing into the IP network, which degrades the real-time transmission performance and creates a fairness problem because of TCP traffic being suppressed. The approach developed is to adapt the transport protocol and the way in which it interacts with the network in order to support voice flows competing with TCP traffic in the Internet environment. We propose a new multiplexing scheme of RTP voice streams called TFMC (TCP-Friendly Multiplexing Control) which uses TCP-frien! dly equation-based congestion control for unresponsive flows. TFMC sender adapts the throughput generated by protocol header in response to congestion while maintaining a steady voice data throughput in order to achieve requirements of voice over IP applications where a smooth sending rate is of importance. We discuss through analytical and simulation results the TFMC scheme performance. Simulations show that the proposed equation for adjusting the number of multiplexed packets achieves efficient voice flow transmission and improves packet delay while being fair to TCP.