We are interested in widening the reasoning support for propositional modal logics in the so-called modal cube. The modal cube consists of extensions of the basic modal logic K with an arbitrary combination of the modal axioms B, D, T, 4 and 5. We revisit recently developed local reductions from all logics in the modal cube to a normal form comprising sets of clausal formulae with associated modal levels. We extend these reductions further to the basic modal logic K, called definitional reductions. This enables any prover for K to be used to solve the satisfiability problem for all logics in the modal cube. We also present alternative, axiomatic, reductions based on ideas originally proposed by Kracht, providing new theoretical results and improved bounds on the size of the reductions. We compare both sets of reductions combined with state-of-the-art provers for K on a large set of parametric benchmarks for all logics in the modal cube. The results show that the provers per- form better with reductions based on the clausal normal form than the axiomatic reductions.