The left ventricular isovolumic pressure decay, obtained by cardiac catheterization, is widely characterized by the time constant τ (tau) of the exponential regression p(t)= P¥+(P0–P¥)exp(–t/τ). However, several authors prefer to prefix P¥=0 instead of coestimating the pressure asymptote empirically; others present τ values estimated by both methods that often lead to discordant results and interpretation of lusitropic changes. The present study aims to clarify the relations between the τ estimates from both methods and to decide for the more reliable estimate. The effect of presetting a zero asymptote on the τ estimate was investigated mathematically and empirically, based on left ventricular pressure decay data from isolated ejecting rat and guinea pig hearts at different preload and during spontaneous decrease of cardiac function. Estimating τ with preset P¥=0 always yields smaller values than the regression with empirically estimated asymptote if the latter is negative and vice versa. The sequences of τ estimates from both methods can therefore proceed in reverse direction if τ and P¥ change in opposite directions between the measurements. This is exemplified by data obtained during an increasing preload in spontaneously depressed isolated hearts. The estimation of the time constant of isovolumic pressure fall with a preset zero asymptote is heavily biased and cannot be used for comparing the lusitropic state of the heart in hemodynamic conditions with considerably altered pressure asymptotes.