As medical ultrasound imaging moves to larger apertures and higher frequencies, tissue sound-speed variations continue to limit resolution. In geophysical imaging, a standard approach for estimating near-surface aberrating delays is to analyze the time shifts between common-midpoint signals. This requires complete data— echoes from every combination of an individual source and receiver. Unfocused, common-midpoint signals remain highly correlated in the presence of aberration; there is also tremendous redundancy in the data. In medical ultrasound, this technique has been impaired by the wide-angle, random-scattering nature of tissue. Until now, it has been difficult to estimate azimuth-dependent aberration profiles or to harness the full redundancy in the complete data. Prefiltering the data with two-dimensional fan filters largely solves these problems, permitting highly overdetermined, least-squares solutions for the aberration profiles at many steering angles. In experiments with a tissue-mimicking phantom target and silicone rubber aberrators at nonzero stand-off distances from a 1-D array transducer, this overdetermined, fan-filtering algorithm (OFF) significantly outperformed other published algorithms.