Many different sources of overheads impact the efficiency of a scheduling strategy applied to a parallel loop within a scientific application. In prior work, we handled these overheads using multiple loop scheduling strategies, with each scheduling strategy focusing on mitigating a subset of the overheads. However, mitigating the impact of one source of overhead can lead to an increase in the impact of another source of overhead, and vice versa. In this work, we show that in order to improve efficiency of loop scheduling strategies, one must adapt the loop scheduling strategies so as to handle all overheads simultaneously. To show this, we describe a composition of our existing loop scheduling strategies, and experiment with the composed scheduling strategy on standard benchmarks and application codes. Applying the composed scheduling strategy to three MPI+OpenMP scientific codes run on a cluster of SMPs improves performance an average of 31% over standard OpenMP static scheduling.