This paper identifies sharp bounds on the mean treatment response and average treatment effect under the assumptions of both concave monotone treatment response (concave-MTR) and monotone treatment selection (MTS). We use our bounds and the US National Longitudinal Survey of Youth to estimate mea… n returns to schooling. Our upperbound estimates are substantially smaller than (1) estimates using only the concave-MTR assumption of Manski (1997) and (2) estimates using only the MTR and MTS assumptions of Manski and Pepper (2000). They fall in the lower range of the point estimates given in previous studies that assume linear wage functions. This is because ability bias is corrected by assuming MTS when the functions are close to linear. Our results therefore imply that higher returns reported in previous studies are likely to be overestimated.