Near-Earth Asteroid (29075) 1950 DA may closely encounter Earth in 2880. The probability of Earth impact may be as high as 1/300, but the outcome of the encounter depends critically on the physical properties of the asteroid [Giorgini et al., 2002. Science 196, 132-136]. We have used Arecibo and Goldstone radar data and optical lightcurves to estimate the shape, spin state, and surface structure of 1950 DA. The data allow two distinct models. One rotates prograde and is roughly spheroidal with mean diameter 1.16 ± 0.12 km. The other rotates retrograde and is oblate and about 30% larger. Both models suggest a nickel-iron or enstatite chondritic composition. Ground-based observations should be able to determine which model is correct within the next several decades.