A steady-state, one-dimensional mathematical model for oxygen transfer in fish gills suggests that under conditions permitting adequate oxygen uptake, the uptake advantage of a counter-current configuration over a co-current configuration is small, given otherwise identical gills, fluid fluxes, and afferent fluid oxygen tensions. The in vivo uptake advantage of a counter-current fish, compared to a hypothetical co-current fish, is estimated from published data on oxygen uptake of three fish species (Chaenocephalus aceratus, Salmo gairdneri, Scyliorhinus stellaris) and found to range from 3 to 17%. However, heuristic calculations assuming Poiseuille flow suggest that a co-current fish would expend more than 46% additional power for respiration to compensate for a 10% uptake advantage enjoyed by an otherwise identical counter-current fish. Thus the importance of counter-current oxygen transfer may lie primarily in its energy economy rather than in the magnitude of the uptake advantage. © 1987 Academic Press Inc. (London) Ltd.