We address the problem of simplifying Morse–Smale complexes computed on volume datasets based on discrete Morse theory. Two approaches have been proposed in the literature based on a graph representation of the Morse–Smale complex (explicit approach) and on the encoding of the discrete Morse gradient (implicit approach). It has been shown that this latter can generate topologically-inconsistent representations of the Morse–Smale complex with respect to those computed through the explicit approach. We propose a new simplification algorithm that creates topologically-consistent Morse–Smale complexes and works both with the explicit and the implicit representations. We prove the correctness of our simplification approach, implement it on volume data sets described as unstructured tetrahedral meshes and evaluate its simplification power with respect to the usual Morse simplification algorithm.