This paper discusses three techniques useful in relaxing the constraints imposed by control flow on parallelism: control dependence analysis, executing multiple flows of control simultaneously, and speculative execution. We evaluate these techniques by using trace simulations to find the limits of parallelism for machines that employ different combinations of these techniques. We have three major results. First, local regions of code have limited parallelism, and control dependence analysis is useful in extracting global parallelism from different parts of a program. Second, a superscalar processor is fundamentally limited because it cannot execute independent regions of code concurrently. Higher performance can be obtained with machines, such as multiprocessors and dataflow machines, that can simultaneously follow multiple flows of control. Finally, without speculative execution to allow instructions to execute before their control dependences are resolved, only modest amounts of parallelism can be obtained for programs with complex control flow.