TCP Low Priority (TCP-LP), a algorithm whose goal is to utilize only the excess network bandwidth as compared to the "fair share" of bandwidth as targeted by TCP. Service prioritization among different traffic classes is an important goal for the Internet. Conventional approaches to solving this problem consider the existing best-effort class as the low-priority class, and attempt to develop mechanisms that provide "better-than-best-effort" service. We explore the opposite approach, and devise a new distributed algorithm to realize a low-priority service (as compared to the existing best effort) from the network endpoints. To this end, we develop TCP Low Priority (TCP-LP), a distributed algorithm whose goal is to utilize only the excess network bandwidth as compared to the "fair share" of bandwidth as targeted by TCP. The key mechanisms unique to TCP-LP congestion control are the use of one-way packet delays for early congestion indications and a TCP-transparent congestion avoidance policy. The results of our simulation and Internet experiments show that: •TCP-LP is largely non-intrusive to TCP traffic. •Both single and aggregate TCP-LP flows are able to successfully utilize excess network bandwidth; moreover, multiple TCP-LP flows share excess bandwidth fairly. •Substantial amounts of excess bandwidth are available to the low-priority class, even in the presence of "greedy" TCP flows. •Despite their low-priority nature, TCP-LP flows are able to utilize significant amounts of available bandwidth in a wide-area network environment.