In a labor market in which firms offer tied hours-wage packages and there is substantial dispersion in the wage offers associated with a particular type of job, the best job available to a worker at a point in time may pay well but require an hours level which is far from the worker's labor supply schedule, or pay poorly but offer desirable hours. Intuitively, one would expect hours constraints to influence the pattern of wage-hours tradeoffs which occur when workers quit to new jobs. Constrained workers may be willing to sacrifice wage gains for better hours. Likewise, workers may accept jobs offering undesirable hours only if the associated wage gains are large. We investigate this issue empirically by examining whether overemployment (underemployment) on the initial job increases (reduces) the partial effect on the wage gain of a positive change in hours for those who quit. We also examine whether overemployment (underemployment) on the new job increases (reduces) the partial effect on the wage gain of a positive change in hours for those who quit. Despite the limitations imposed by small sample sizes and lack of information on the magnitude of hours constraints, our results support the view that an individual requires compensation to work in jobs which, given the individual's particular preferences, offer unattractive hours.