The perception of sound distance has been sparsely studied so far. It is assumed to depend on familiar loudness, reverberation, sound spectrum, and parallax, but most of these factors have never been carefully addressed. Reverberation has been mostly analyzed in terms of ratio between direct and indirect sound, and total duration. Here we were interested in assessing the impact of each reflection order on distance localization. We compared sound source discrimination at an intermediate and at a distant location with direct sound only, one, two, three, and four reflection orders in a 2AFC task. At the intermediate distances, normalized psychophysical curves reveal no differentiation between direct sound and up to three reflection orders, but sounds with four reflection orders have significantly lower thresholds. For the distant sources, sounds with four reflection orders yielded the best discrimination slopes, but there was also a clear benefit for sounds with three reflection orders. We discuss the results in terms of direct-to-reflected ratio, reflection directionality, and spectral information.