An end-to-end "foreground/background" priority scheme is useful for end hosts to utilize the residual capacity left unused by high-priority foreground applications. Several end-to-end prioritization schemes, such as TCP-LP (Low Priority) and TCP-Nice, have been proposed, however, the residual capacity cannot be fully utilized by these schemes. We propose TCP Westwood Low Priority (TCPW-LP), a scheme that maximizes the utilization of residual capacity without intrusion on coexisting foreground flows. TCPW-LP employs an "Early Window Reduction" mechanism to reduce its congestion window as a reaction to incipient congestion. To achieve high efficiency, the reaction is based on the estimation whether the congestion is caused by the foreground traffic or not. Simulation results show that TCPW-LP appropriately defers to foreground flows. Further, under a wide range of buffer capacity and link error losses, TCPW-LP better utilizes the residual capacity than other proposed priority schemes or even TCP Reno.