We report first results from our extensive survey of the very small (H>21.5mag) near-Earth asteroids. Our aim was to obtain photometric lightcurves for these faint, fast moving objects and to measure their rotation periods and amplitudes of light variations. These parameters can be used to make statistical analysis of the still little known population of the smallest asteroids, test present theories of the YORP effect as well as to study their spin limits, which are connected with their internal structure. Due to the faintness of the targets and the expected short periods of rotation, observations were performed with the large, 10-m SALT telescope in SAAO (South Africa). For most asteroids, V filter images with exposure times of 5-60 seconds were obtained with the instrument's SALTICAM's CCD camera. Even though the non-sidereal tracking was not available, the SALTICAM's relatively large field-of-view of 8'x8' helped to perform the relative photometry of the fast-moving targets. The presented asteroids have synodic periods ranging from 77s to 44min, effective diameters from 21 to 94m, and significantly elongated shapes.