A set of experiments was conducted to examine the loudness of sounds with temporally asymmetric amplitude envelopes. Envelopes were generated with fast-attack/slow-decay characteristics to produce F-S (or "fast-slow") stimuli, while temporally reversed versions of these same envelopes produced corresponding S-F ("slow-fast") stimuli. For sinusoidal (330-6000 Hz) and broadband noise carriers, S-F stimuli were louder than F-S stimuli of equal energy. The magnitude of this effect was sensitive to stimulus order, with the largest differences between F-S and S-F loudness occurring after exposure to a preceding F-S stimulus. These results are not compatible with automatic gain control, power-spectrum models of loudness, or predictions obtained using the auditory image model [Patterson et al., J. Acoust. Soc. Am. 98, 1890-1894 (1995)]. Rather, they are comparable to phenomena of perceptual constancy, and may be related to the parsing of auditory input into direct and reverberant sound.