We report the results of the Small Main-Belt Asteroid Lightcurve Survey, the first dedicated survey to measure the rotational light-curve properties of main-belt asteroids having diameters smaller than 5 km. Physical studies of asteroids in this size range are critical for investigating the origin of similar diameter near-Earth asteroids. In addition, these small asteroids place important constraints on asteroid collisional evolution models. Using charge-coupled device (CCD) detectors on 1- and 2-m class telescopes, we measured lightcurves for 32 small main-belt asteroids. Two of these objects were new discoveries made during the course of the survey. One additional object, a 25-km-diameter Trojan, was also discovered and observed. Objects in our new sample (mean diameter, 3 km) have a mean rotational frequency faster than that of larger main-belt asteroids. Their lightcurve amplitudes are similar, however, which implies that there is no significant size dependence on the shapes of collisional fragments over the range of 3 to 50 km. We detected the second shortest rotation period currently known, 2.35 hr, suggesting a density of ≥2 g cm -3 for an unstressed interior. The lack of substantially faster rotation periods could indicate that small asteroids have weak or fractured interiors. All lightcurves were investigated for nonperiodic variations due to free precession, possibly observable for some small asteroids. Although such motion could not be ruled out in all cases, no conclusive detection of free precession was made.