  We study the properties of a photodetector that has a number-resolving
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 {\em 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.
