We analyze demand substitution relationships among fish in the snapper/grouper complex in the southeast United States. Monthly data from 1977 to 1992 are used to form a set of six fish aggregates. The dockside demands are analyzed in an empirical inverse demand system, developed for the purposes of this study. Attention is paid to consistency of the system with the theory of demand, to functional form flexibility, and to consistent estimation of parameters. Empirical results imply that the demands have small quantity elasticities, which can be thought of as high price elasticities in a direct demand system. Regulatory variations in landed quantities have little measured effect on prices, implying that market prices are good per-unit measures of the welfare costs of catch restrictions to consumers. Welfare estimates of hypothetical harvest reductions are computed and illustrated.