In order to sustain exercise immediately following exhaustive cycle ergometry, the external power output (P) needs to be reduced below the subject’s critical power (CP) (Coats et al., 2003): CP being the asymptote of the hyperbolic power-duration relationship (P-t_lim), which is also defined by a curvature constant, W′, equivalent to a fixed amount of work that can be performed above CP (Poole et al., 1988). This is consistent with a W′ ‘depletion’ mediated intolerance – supra-CP exercise is then only feasible with, at least partial, W′ replenishment. That some subjects cannot sustain even sub-CP exercise following exhaustion (Coats et al., 2003) suggests that the preceding exercise may reduce CP and constrain W′ repletion. We therefore aimed to estimate the P-t_lim relationship, together with pulmonary O₂ uptake (VO₂), across a range of recovery work-rates following exhaustion. We hypothesised that CP would be reduced following recovery at high (95% CP) but not low work-rates. Six healthy men (23 ± 5 yrs; mean ± SD) gave informed consent to perform: 1) incremental-ramp cycle ergometry for estimation of the lactate threshold (LT); 2) 4 different high-intensity constant-P tests (CON), each on separate days and taken to the tolerable limit, to estimate VO_2max and establish the P-t_lim parameters (CP and W′); 3) a 10 min constant-P test at CP. CP and W′ were also estimated after each of three 6 min recovery bouts (REC) from exhaustive exercise (~6 min): 20 W, 105% LT and 95% CP. Gas-exchange was measured breath-by-breath by mass-spectrometry and turbinometry (MSX, Morgan Medical, UK). At the tolerable limit of all exercise bouts, VO₂ attained maximum (4.13 ± 0.43 l.min^-1). Whereas CP (CON: 242 ± 27 W) was unchanged in REC (240 ± 28, 239 ± 25, 243 ± 31 W at 20 W, 105% LT, and 95% CP, respectively), W′ (CON: 20.1 ± 4.9 kJ) was progressively reduced the higher the recovery P (REC: 10.9 ± 2.6, 8.2 ± 1.5, and 2.8 ± 2.1 kJ). VO₂ recovery during REC was also dependent on recovery P (reaching 1.13 ± 0.13, 2.45 ± 0.35, and 3.68 ± 0.39 l.min^-1, respectively), but was not well correlated with W′: the repletion of which was appreciably attenuated during high P recovery. Therefore, these data suggest that neither prior exhaustive exercise nor recovery P affect CP. However, because VO₂ during REC 95% CP remained above (p < 0.05; t-test) the 10 min CP value (3.48 ± 0.38 l.min^-1) this suggests that the metabolic equivalent of CP may be increased during high P recovery, and limit W′ restoration. Exercise tolerance following exhaustion therefore, presumably depends on the degree to which the external power requirement and its metabolic equivalent are reduced at the tolerable limit.