It is commonly argues that reducing the number of hours worked by the employed would lead to lower unemployment, since firms will respond by hiring more workers. This paper examines the relationship between hours worked and unemployment, in the context of an efficiency wage model where involuntary unemployment occurs owing to imperfect monitoring of worker effort. The first part of the paper presents a partial equilibrium model where the number of hours worked per week is determined exogenously. The model makes standard assumptions about effort costs (i.e., increasing marginal disutility of work), and also allows for the presence of daily 'set-up costs' for the worker. It is shown that under these assumptions the equilibrium level of unemployment, viewed as a function of hours worked, is 'U-shaped' (or simply increasing, if the set-up costs are zero). The paper then moves to a general equilibrium framework where hours are determined endogenously; it is shown that in this case the free market choice of hours is always greater than the unemployment-minimizing level, so that 'work-sharing' could indeed lower unemployment. However the paper also presents a powerful and surprising welfare result: conditional on being unemployed, a representative worker is always best off under the free market outcome. Nonetheless, starting from the free market equilibrium there is always an hours-reduction policy which reduces unemployment and increases the expected utility of a currently unemployed worker. The currently employed are always made worse off by such a policy.