We present Dubstep, a novel system that uses the find transform-navigate approach to automatically explore new parallelization opportunities in already parallelized (fullysynchronized) programs by opportunistically relaxing synchronization primitives. This set of transformations generates a space of alternative, possibly non-deterministic, parallel programs with varying performance and accuracy characteristics. The freedom to generate parallel programs whose output may differ (within statistical accuracy bounds) from the output of the original program enables a significantly larger optimization space. Dubstep then searches this space to find a parallel program that will, with high likelihood, produce outputs that are acceptably close to the outputs that the original, fully synchronized parallel program would have produced. Initial results from our benchmarked application show that Dubstep can generate acceptably accurate and efficient versions of a parallel program that occupy different positions in performance/accuracy trade off space.