We estimate a labor supply model that permits hours restrictions of a simple but general form. Each individual chooses from among a finite set of jobs drawn at random from a market distribution, each offering a fixed quantity of hours. The polar cases of no constraints on hours worked and exogenous hours are nested within the general case. Our results are consistent with a substantial amount of rationing in the work hours of a sample of low-income men, most of whom are working less than they would like.