In this paper we analyze the effect of compiler optimizations on fine grain parallelism in scalar programs. We characterize three levels of optimization: classical, superscalar, and multiprocessor. We show that classical optimizations not only improve a program's efficiency but also its parallelism. Superscalar optimizations further improve the parallelism for moderately parallel machines. For highly parallel machines, however, they actually constrain available parallelism. The multiprocessor optimizations we consider are memory renaming and data migration.