C++11 Most accurate way to pause execution for a certain amount of time?

I'm currently working on some C++ code that reads from a video file, parses the video/audio streams into its constituent units (such as an FLV tag) and sends it back out in order to "restream" it.

Because my input comes from file but I want to simulate a proper framerate when restreaming this data, I am considering the ways that I might sleep the thread that is performing the read on the file in order to attempt to extract a frame at the given rate that one might expect out of typical 30 or 60 FPS.

One solution is to use an obvious std::this_thread::sleep_for call and pass in the amount of milliseconds depending on what my FPS is. Another solution I'm considering is using a condition variable, and using std::condition_variable::wait_for with the same idea.

I'm a little stuck, because I know that the first solution doesn't guarantee exact precision -- the sleep will last around as long as the argument I pass in but may in theory be longer. And I know that the std::condition_variable::wait_for call will require lock reacquisition which will take some time too. Is there a better solution than what I'm considering? Otherwise, what's the best methodology to attempt to pause execution for as precise a granularity as possible?