Medical ultrasonic images are degraded by tissues with inhomogeneous acoustic velocities. The resulting phase aberration raises the off-peak response of the imaging system's point spread function (PSF), decreasing dynamic range. In extreme cases, multiple images of a single target are displayed. Phase aberration may become a limiting factor to image quality as ultrasonic frequency and aperture size are increased in order to improve spatial resolution. A method is proposed to correct for unknown phase aberration, which uses speckle brightness as a quality factor. The phase delays of a phased array transducer are modified, element by element, to maximize mean speckle brightness in a region of interest. The technique proposed is analogous to the correction technique used by Muller and Buffington [J. Opt. Soc. Am. 64 (9), 1200-1209 (1974)] to adaptively focus incoherent optical telescopes. The method is demonstrated using a computer model with several different simulated aberration profiles. With this model, mean speckle brightness is calculated using the two-dimensional PSF. Experiments have also been conducted in which speckle brightness is shown to increase as the phase delays of an ultrasonic scanner are modified in order to compensate for a rippled aberrating layer made of silicone rubber. The characteristics of the proposed method, and the possibility of employing it clinically to correct for unknown inhomogeneities in acoustic velocity, are discussed.