We present a method and a software tool, the FrameNet Transformer, for deriving customized versions of the FrameNet database based on frame and frame element relations. The FrameNet Transformer allows users to iteratively coarsen the FrameNet sense inventory in two ways. First, the tool can merge entire frames that are related by user-specified relations. Second, it can merge word senses that belong to frames related by specified relations. Both methods can be interleaved. The Transformer automatically outputs format-compliant FrameNet versions, including modified corpus annotation files that can be used for automatic processing. The customized FrameNet versions can be used to determine which granularity is suitable for particular applications. In our evaluation of the tool, we show that our method increases accuracy of statistical semantic parsers by reducing the number of word-senses (frames) per lemma, and increasing the number of annotated sentences per lexical unit and frame. We further show in an experiment on the FATE corpus that by coarsening FrameNet we do not incur a significant loss of information that is relevant to the Recognizing Textual Entailment task.