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The Benjamini-Hochberg procedure and related methods are classical methods for controlling the false discovery rate for multiple testing problems. These procedures were originally designed for continuous test statistics. However, in many applications, the test statistics are discretely distributed. While it is well known that e.g. the Benjamini-Hochberg procedure still controls the false discovery rate in the discrete paradigm, it may be unnecessarily conservative. Thus, there is interest in developing more powerful FDR procedures for discrete data. In this talk we aim to improve the classical procedures in such settings by incorporating the discreteness of the p-value distributions. We investigate the performance of these approaches for high-dimensional empirical and simulated data. Joint work with Etienne Roquain and Guillermo Durand.