Migrating birds often alternate between flight steps, when distance is covered and energy consumed, and stopover periods, when energy reserves are restored. An alternative strategy is fly-and-forage migration, useful mainly for birds that hunt or locate their prey in flight, and thus, enables birds to combine foraging with covering migration distance. The favourability of this strategy in comparison with the traditional stopover strategy depends on costs of reduced effective travel speed and benefits of offsetting energy consumption during migration flights. Evaluating these cost-benefit effects, we predict that fly-and-forage migration is favourable under many conditions (increasing total migration speed), both as a pure strategy and in combination with stopover behaviour. We used the osprey (Pandion haliaetus) as test case for investigating the importance of this strategy during spring and autumn migration at a lake in southern Sweden. The majority, 78%, of passing ospreys behaved according to the fly-and-forage migration strategy by deviating from their migratory track to visit or forage at the lake, while 12% migrated past the lake without response, and 10% made stopovers at the lake. Foraging success of passing ospreys was almost as good as for birds on stopover. Timing of foraging demonstrated that the birds adopted a genuine fly-and-forage strategy rather than intensified foraging before and after the daily travelling period. We predict that fly-and-forage migration is widely used and important among many species besides the osprey, and the exploration of its occurrence and consequences will be a challenging task in the field of optimal migration.