Static scheduling of independent, moldable tasks on parallel machines with frequency scaling comprises decisions on core allocation, assignment, frequency scaling and ordering, to meet a deadline and minimize energy consumption. Constraining some of these decisions reduces the solution space, i.e. may increase energy consumption, but may also open the path to new, near-optimal approaches. We investigate how constraints of different steps influence energy consumption, starting with an unrestricted scheduler for moldable tasks. The constraints are partly derived from existing schedulers, but also generalized in a systematic way. We present integer linear programs for all scheduling variants. We compare energy consumption of schedules for a benchmark suite of synthetic task sets of different sizes and for task sets derived from real applications. In addition, we check how close the results are to the optimum results when the ILP solver meets a timeout. Our results indicate that constraints on task execution order, which avoid explicit representation of task order in ILPs, are mostly responsible for near-optimal energy consumption among large task sets. Furthermore, we find that for all steps except allocation, non-optimal fast heuristics can be used without sacrificing too much energy for the resulting schedule. Finally, we can show that an ILP for a new scheduler, for which also a heuristic version exists, is comparable in quality to more complicated schedulers.