The loudness of tones that change continuously in level over time was studied using magnitude estimation and a delayed loudness-balance procedure. In the magnitude estimation task, subjects estimated the loudness of continuous and intermittent 1000-Hz tones that either increased or decreased continuously in level over roughly 3 min. Two stimulus ranges were used: 30 to 70 and 50 to 90 dB SPL. For the low-level conditions, the results are essentially identical to those of Canevet and Scharf [J. Acoust. Soc. Am. 88, 2136-2142 (1990)], who ran similar conditions. Tones that increased in level changed in loudness as a function of SPL at a slower rate than tones that decreased in level. For the high-level conditions, the same result was obtained, but the magnitude of the difference among conditions is smaller. A delayed loudness-matching procedure was used to measure the physical magnitude corresponding to loudness differences among a subset of the conditions. Judged equal-loudness levels showed a sharp decline in loudness for conditions with tones that decreased continuously in level, but the magnitude of the reduction was less than that interpolated from magnitude estimates for identical stimuli. The source of the difference is unclear. To explore the role of cognitive influences, subjects' attention was diverted by a video word-identification task during the period of adaptation. For this task, the loudness decline was reduced for loudness balances and magnitude estimations compared to conditions where attention was concentrated on the adapting stimulus. In another magnitude-estimation task, the loudness decline for monaural stimulation was found to occur only in the 'adapted' ear. In aggregate, these findings lend additional support to the notion that the effect is a sensory phenomenon, with a substantial portion mediated by a central mechanism.