We study the properties of a photodetector that has a numberresolving capability. In the absence of dark counts, due to its finite quantum efficiency, photodetection with such a detector can only eliminate the possibility that the incident field corresponds to a number of photons less than the detected photon number. We show that such a non-photon number-discriminating detector, however, provides a useful tool in the reconstruction of the photon number distribution of the incident field even in the presence of dark counts.