The tolerable duration (t) of muscular exercise in the very heavy intensity domain has been well described as a hyperbolic function of the external power (P), with an asymptote termed critical power (CP) and a curvature constant W’, in units of work (intriguingly), equivalent to a constant amount of work that can be performed above CP (e.g. Poole et al. 1988). This is notionally consistent with the tolerable duration of supra-CP exercise being dependent on the ‘utilisation’ rate of W’, with the tolerable limit being attained when this apparent ‘store’ is depleted. However, establishing the physiological correlate(s) of this ‘store’ is complicated by the difficulty in resolving the profile of W’ depletion during the exercise. In order gain insight into this issue, we determined the relationship between the recovery kinetics of W’ following exhausting exercise concomitantly with those of oxygen uptake ([vdot]O₂) and blood [lactate], and subsequent exercise tolerance. Following ethical committee approval, 6 healthy males (24±4 yr) each performed, on separate occasions, a ramp-incremental and 4 different constant-load (CON) high-intensity exercise tests to the limit of tolerance on a computer-controlled electromagnetically-braked cycle ergometer for determination of CP, W’ and [vdot]O_2max. Subsequently, a further 3 constant-load tests were performed (REC), each at a different work rate and each preceded by a supra-CP exercise bout to the limit of tolerance (chosen to elicit fatigue in 6 min) with recovery periods of 2, 6 and 15 min at 20W. Gas exchange was measured breath-by-breath, and finger-tip blood sampled at discrete points for [lactate] analysis. Relative to CON, the REC protocols had no significant effect on [vdot]O_2max (CON vs REC (SD): 3.81±0.52 vs 3.71±0.47 l min^-1), CP (212±34 vs 213±33 W) or [lactate] at the limit of tolerance (10.11±1.02 vs 10.46±1.22 mM). The hyperbolic P-t relationship was retained in the REC studies, with CP being unchanged but W’ being highly dependent on the duration of the intervening recovery phase: i.e. W’ recovered to 37±5%, 65±6% and 86±4% of the CON value following 2, 6 and 15-min of recovery, respectively. The recovery kinetics of W’ (interpolated t_1/2 = 234±32s) did not cohere well with those of [vdot]O₂ (t_1/2 = 74±2s) or [lactate] (t_1/2 = 1366±799s). In conclusion, the finding that the P-t relationship remained hyperbolic during REC, with no change in CP, supports the notion that the W’ depletion profile ‘shapes’ the high-intensity exercise tolerance. Comparisons of the utilization and recovery kinetics of W’ with those of the metabolic end-products may aid in clarifying not only its role as a parameter determining the tolerance for high-intensity exercise but what, physiologically, it’s determinants actually are!