We present a structural empirical job search model: job offers arrive randomly from a joint wage-hours offer distribution. The unemployed accept a job if its utility level is higher than the reservation utility level. Specific attention is paid to identification, since the observed (accepted) hours distribution is determined both by the hours offer distribution and by the job acceptance probability. To identify the hours offers from the optimal hours, defined by preferences, we use information on desired working hours. We estimate several model variants: a base specification with only information on observed working hours, and different variants with desired hours, which allow for different interpretations of desired hours by survey respondents or for differences in the distribution of measurement error in desired hours. We compare the various specifications on basis of differences in the fit and on basis of differences in policy relevant elasticities.