We derive the theoretical upper limit for concentration of direct solar radiation at low latitudes with nontracking concentrators from the projected solid angle sampled by the apparent motion of the sun, for the case where the energy efficiency is referred to the energy incident on the entrance aperture. Based on the fact that the solar radiation is not uniformly distributed within this projected solid angle and that the apparent solar motion is known, we derive the optimal acceptance as a function of direction and time, which means rejecting the lower density radiation and switching off the device when losses would be higher than gains. Just as a device may gain concentration by rejecting radiation from certain directions, it can also gain by not operating at all, thus avoiding losses at certain times. Trough-type systems, which have translational symmetry, cannot be ideal nontracking concentrators, but for low losses they perform only slightly worse than general three-dimensional concentrators.