When individual vessel quotas are used in fisheries management, quotas are set species by species, in most cases. Often, it is only the most important of the target species that are regulated by quota. There is a growing concern that the introduction of individual vessel quotas leads to increased fishing pressure on unregulated species. To model the behavior of fishermen with this regulatory structure, a constrained profit function is used, where the quota species are treated as fixed, while the unregulated species are variable. An empirical analysis is provided for Norwegian purse seiners.