Stream programming abstracts parallelism complexity by modeling a program as a set of streaming tasks. Tasks run repeatedly and can even be internally parallel, i.e., use one or multiple cores simultaneously (moldable). The throughput of the streaming application, as well as its energy consumption, depends strongly on scheduling, i.e., on how tasks are mapped to cores, and on the frequency at which they run. Crown scheduling is a scheduling method that reduces this problem's combinatorial complexity considerably by introducing a few additional restrictions especially on tasks' core allocation sizes and mapping. While it has previously been shown to outperform competing methods, the impact of these restrictions on the schedule quality has, up to now, never been analyzed quantitatively. In this paper, we first propose several crown scheduler improvements toward fewer restrictions. Also, we provide an Integer Linear Programming formulation that solves the same optimization problem without the inherent restrictions of crown scheduling. While in an extreme case an unrestricted schedule might use 3.7 times less energy than a crown schedule for a realistic execution platform model, we show that in practical benchmarks the difference is small while crown schedulers are significantly faster than unrestricted scheduling. We experimentally confirm this with benchmarks derived from random task collections, classic parallel algorithms as well as the Streamit benchmark suite.