We tested the hypothesis that birds are selected to minimize the time spent on migration, that is, to migrate as fast as possible. Optimal fat loads in time-selected migration were predicted for different rates of fat accumulation at stopover sites. We analyzed departure fat loads of migrating bluethroats Luscinia svecica svecica, experimentally provided with extra food at a stopover site, and of migrating rufous hummingbirds Selasphorus rufus, which showed considerable individual variation in fat-deposition rate, in relation to these predictions. We found qualitative agreement with the time-minimization hypothesis. However, quantitative agreement requires that specific assumptions be fulfilled for both species: (1) consistent differences in expected speed of migration should exist between different individuals of the same species and/or (2) the expected speed of migration should increase along the route Both of these assumptions are probably valid, and ringing data suggest an increase in bluethroat autumn migration speed along the route Physiological and flight mechanical constraints will prevent birds from depositing excessively large amounts of fuel. These assumptions and constraints should be taken into account in future critical tests of the hypothesis that natural selection operates to maximize the speed of migration.