In this paper, we develop and evaluate methods for decomposing complex questions for a question answering system to less complex questions. This aims at increasing the number of correct answers, especially in (deep) semantic question answering systems. For example, an event that occurs as a temporal restriction of a question can be queried for its date and the resulting answer can be substituted in the original question leading to a simpler, revised question. We present six decomposition classes, which are employed for annotating the 996 different German QA@CLEF questions from 2004 till 2008 and trigger different decomposition methods. Most methods work on the level of semantic representations, thereby avoiding natural language generation, a second parsing step, and possible errors in these two steps. The decomposition classes are not equally distributed, but three of them occur frequently in the questions. In the evaluation, the precision and recall for automatically classifying questions with respect to the decomposition classes are investigated. Then, the impact on a deep question answering system is determined. On the QA@CLEF questions, which by construction prefer questions that can be answered from single sentences, the performance gain in number of correct answers is not large, but significant. This encourages us to develop and test further decomposition classes and methods as future work.