Bycatch of unwanted, prohibited, or protected species is a problem in most commercial fisheries. Trawl fisheries are particularly prone to bycatch problems because trawls are not species-selective. In this paper, I review the history of finfish bycatch research in the Gulf of Mexico shrimp trawl fishery and explore the use of quotas to reduce finfish bycatch by examining four. sheries that currently use bycatch quotas: ( 1) the arrow squid trawl fishery of New Zealand, which uses fleet bycatch quotas for sea lion bycatch, ( 2) the Alaskan ground fish trawl. sheries, which use fleet quotas under a "vessel incentive program'' for prohibited species, ( 3) the ground fish trawl fishery of British Columbia, Canada which uses individual vessel bycatch quotas for prohibited species, and ( 4) the multi-species trawl. sheries of New Zealand, which use catch balancing, or individual transferable quotas, for most commercially landed species. Based on the bycatch quota experiences in these. sheries, elements of successful bycatch quota programs include: ( 1) individual accountability, in the form of individual or cooperative bycatch quotas, rather than fleet quotas, ( 2) 100% observer coverage, ( 3) relatively small, manageable fleets, ( 4) limited landing ports that can be easily monitored, particularly if observer coverage is incomplete, ( 5) reliable enforcement, ( 6) penalties that are true disincentives, and ( 7) some flexibility in the system for fishermen to have alternatives to manage their bycatch. The Gulf of Mexico shrimp trawl fishery, with an estimated 20,000 licensed boats, is currently too large for individual bycatch quotas to be practical, although individual or cooperative bycatch quotas would be excellent strategies for reducing the bycatch of a smaller fleet. Mobile closed areas might be beneficial for reducing the bycatch of particular species, but these shortterm closures would require real-time monitoring of bycatch rates and vessel monitoring systems on all vessels. However, under any management regime, incentives and/or rigorously enforced disincentives are the key to successful bycatch reduction.