O-2 uptake in the lungs, and therefore arterial oxygenation, is favored by a low Hb-P-50 but this inhibits tissue O-2 extraction, raising the question of optimal P-50 during maximal exercise when (V) over dot (O2) is limited by O-2 supply. Using a model of the lungs and muscles connected by the circulation so that O-2 transport is simultaneously considered in both sites, sensitivity of(V) over dot (O2max) to P-50 was determined at three altitudes: PB = 760, 464 and 253 Torr, encompassing sea level and Mt. Everest. At PB = 760 Torr, (V) over dot (O2max) peaked at P-50 = 30 Torr, was 99.4% (of that at 30) at normal P-50 (26.8) and exceeded 95% (of that at P-50 = 30) over the P-50 range from 24 to 43 Torr. Optimal P-50 at PB = 464 Torr was 25 Torr, (V) over dot (O2max) at P-50 = 26.8 was reduced only 0.1% and exceeded 95% over the P-50 range from 19 to 41 Torr. At PB = 253, optimal P-50 was 20 Torr, (V) over dot (O2max) at P-50 = 26.8 was reduced only 0.4% and exceeded 95% over the wide P-50 range from 15 to 47 Torr. While this analysis shows that technically, optimal P-50 falls with altitude, (V) over dot (O2max) is insensitive to P-50 over a range that widens with altitude, so that P-50 changes over a realistic interval would not measurably affect (V) over dot (O2max). (C) 1997 Elsevier Science B.V.