In this paper, we consider the problem of constructing confidence intervals for a population median when the underlying population is discrete. We describe seven methods of assigning confidence levels to order statistic based confidence intervals, all of which are easy to implement. An extensive simulation study shows that, with discrete populations, it is possible to obtain consistently more accurate confidence levels and shorter intervals compared to the ones reported by the classical method which is implemented in commercial softwares. More precisely, the best results are obtained by inverting a two-tailed sign test that properly takes into account tied observations. Some real data examples illustrate the use of these confidence intervals.