We present a novel algorithm for generating state spaces of asynchronous systems using Multi-valued Decision Diagrams. In contrast to related work, we encode the next-state function of a system not as a single Boolean function, but as cross-products of integer functions. This permits the application of various iteration strategies to build a system’s state space. In particular, we introduce a new elegant strategy, called saturation, and implement it in the tool SMART. On top of usually performing several orders of magnitude faster than existing BDD-based state-space generators, our algorithm’s required peak memory is often close to the final memory needed for storing the overall state space.