Speculative parallelization divides a sequential program into possibly parallel tasks and permits these tasks to run in parallel if and only if they show no dependences with each other. The parallelization is safe in that a speculative execution always produces the same output as the sequential execution.In this paper, we present the dependence hint, an interface for a user to specify possible dependences between possibly parallel tasks. Dependence hints may be incorrect or incomplete but they do not change the program output. The interface extends Cytron's do-across and recent OpenMP ordering primitives and makes them safe and safely composable. We use it to express conditional and partial parallelism and to parallelize large-size legacy code. The prototype system is implemented as a software library. It is used to improve performance by nearly 10 times on average on current multicore machines for 8 programs including 5 SPEC benchmarks.