The fuzzy judgement model of Ward (1979) predicts an inverse relation between the amount of stimulus information available to subjects and the magnitude of sequential dependencies on previous stimuli and responses in psychophysical scaling tasks. Ward confirmed this prediction for magnitude estimations of interdot distance for previous responses but not for previous stimuli, although the inverse relation has been repeatedly reported for both the previous stimuli and responses in absolute identification (e.g., Mori, 1989). This paper further explores this seemingly puzzling contradiction. A magnitude estimation of loudness experiment was conducted in which the amount of stimulus information available to subjects was manipulated by a modified version of informational masking (Watson, 1987). An absolute-identification-with-feedback experiment was also conducted to check the effectiveness of the informational masking in reducing the amount of stimulus information. The results of the magnitude estimation experiment show a striking similarity with those of Ward and generalize the failure of sequential dependencies on previous stimuli to vary inversely with stimulus information. An additional assumption that judgement strategies are altered under low-information conditions is necessary to explain this result.