Conventional models of bird flight combine metabolic, mechanical, and aerodynamic components to calculate the rate of fuel consumption and power required for flight, from which we may derive the optimal speeds flying animals should use in different situations. These models contain the implicit assumption that the metabolic and mechanical components of power output are constant and show no systematic variation with speed. This assumption underlies the optimum flight speeds, optimum climb protocol, maximum endurance and maximum flight range predicted by these models. Here we consider alternatives to the assumption that power is independent of speed and show that if the aerodynamic power output from a constant rate of fuel consumption varies with flight speed, then the optima derived from current models of animal flight need to be revised. In some cases (e.g. optimum flight speeds) the current models give answers that are only quantitatively wrong, but in some cases (e.g. optimal cruising altitude) current models give answers that are qualitatively wrong.