Preprocessing turned out to be an essential step for SAT, QBF, and DQBF solvers to reduce/modify the number of variables and clauses of the formula, before the formula is passed to the actual solving algorithm. These preprocessing techniques often reduce the computation time of the solver by orders of magnitude. In this paper, we present the preprocessor HQSpre that was developed for Dependency Quantified Boolean Formulas (DQBFs) and that generalizes different preprocessing techniques for SAT and QBF problems to DQBF. We give a presentation of the underlying theory together with detailed proofs as well as implementation details contributing to the efficiency of the preprocessor. HQSpre has been used with obvious success by the winners of the DQBF track, and, even more interestingly, the QBF tracks of QBFEVAL’18.