Although it is well-known that every satisfiable formula in Lukasiewicz' infinite-valued logic L-infinity can be satisfied in some finite-valued logic, practical methods for finding an appropriate number of truth degrees do currently not exist. As a first step towards efficient reasoning in L-infinity, we propose a method to find a tight upper bound on this number which, in practice, often significantly improves the worst-case tipper bound of Aguzzoli et al.