Recording of digital holograms of a weak signal [0.44 counts per second (cps)] hidden below the detector's noise (21 cps) is investigated by employing the high dynamic range of a photon-counting detector. Recording conditions are discussed in terms of the most important holographic measures, namely, the fringe visibility (or contrast) and signal-to-noise ratio (SNR), and in relation to the main holographic parameters. Theoretically evaluated curves are tested by recording holograms for a wide range of the parameter values. We found that (i) the optimum set of holographic parameters can be determined for a harsh signal conditions, (ii) increasing the visibility does not necessarily improve the more important SNR, and (iii) in cases of nearly constant visibility, the SNR clearly reveals differences in the quality of holographic recordings.