We present two complementary algorithms suitable for using focal-plane measurements to control a wavefront corrector with an extremely high spatial resolution. The algorithms use linear approximations to iteratively minimize the aberrations seen by the focal-plane camera. The first algorithm, Fast & Furious (FF), uses a weak-aberration assumption and pupil symmetries to achieve fast wavefront reconstruction. The second algorithm, an extension to FF, can deal with an arbitrary pupil shape; it uses a Gerchberg-Saxton style error reduction to determine the pupil amplitudes. Simulations and experimental results are shown for a spatial light modulator controlling the wavefront with a resolution of 170 x 170 pixels. The algorithms increase the Strehl ratio from åisebox-0.5ex~0.75 to 0.98-0.99, and the intensity of the scattered light is reduced throughout the whole recorded image of 320 x 320 pixels. The remaining wavefront rms error is estimated to be i̊sebox-0.5ex~0.15 rad with FF and rs̊ebox-0.5ex~0.10 rad with FF-GS.