Task-selection policies are critical to the performance of any architecture that uses speculation to extract parallel tasks from a sequential thread. This paper demonstrates that the immediate postdominators of conditional branches provide a larger set of parallel tasks than existing task-seletion heuristics, which are limited to programming language constructs (such as loops or procedure calls). Our evaluation shows that postdominance-based task selection achieves, on average, more than double the speedup of the best individual heuristic, and 33% more speedup than the best combination of heuristics. The specific contributions of this paper include, first, a description of task selection based on immediate postdominance for a system that speculatively creates tasks. Second, our experimental evaluation demonstrates that existing task-selection heuristics based on loops, procedure calls, and if-else statements are all subsumed by compilergenerated immediate postdominators. Finally, by demonstrating that dynamic reconvergence prediction closely approximates immediate postdominator analysis, we show that the notion of immediate postdominators may also be useful in constructing dynamic task selection mechanisms.