A survey to obtain photoelectric lightcurves of small main-belt asteroids was conducted from November 1981 to April 1982 using the 0.91- and 2.1-m telescopes at the University of Texas McDonald Observatory. A total of 18 main-belt asteroids having estimated diameters under 30 km were observed with over half of these being smaller than 15 km. Rotational periods were determined or estimated from multiple nights of observation for nearly all of these yielding a sample of 17 small main-belt asteroids which is believed to be free of observational selection effects. All but two of these objects were investigated for very short periods in the range of 1 min to 2 hr using power spectrum analysis of a continuous set of integrations. No evidence for such short periods was seen in this sample. Rotationally averaged B(1,0) magnitudes were determined for most of the surveyed asteroids, allowing diameter estimates to be made. Imposing the suspected selection effects of photographic photometry on the results of this survey gives excellent agreement with the results from that technique. This shows that the inability of photographic photometry to obtain results for many asteroids is indeed due to the rotational parameters of those asteroids.