This article revisits the problem of decomposing a Petri net into a network of automata, a problem that has been around since the early 70s. We reformu-late this problem as the transformation of an ordinary, one-safe Petri net into a flat, unit-safe NUPN (Nested-Unit Petri Net) and define a quality criterion based on the number of bits required for the structural encoding of markings. We propose various transformation methods, all of which we implemented in a tool chain that combines NUPN tools with third-party software, such as SAT solvers, SMT solvers, and tools for graph colouring and finding maximal cliques. We perform an extensive evaluation of these methods on a collection of more than 12,000 nets from diverse sources, including nets whose marking graph is too large for being explored exhaustively.