C++ – How to implement an accurate (but variable) FPS limit/cap in the OpenGL application

I am currently working on an OpenGL application to display a few 3D spheres to the user, which they can rotate, move around, etc. That being said, there's not much in the way of complexity here, so the application runs at quite a high framerate (~500 FPS).

Obviously, this is overkill – even 120 would be more then enough, but my issue is that running the application at full-stat eats away my CPU, causing excess heat, power consumption, etc. What I want to do is be able to let the user set an FPS cap so that the CPU isn't being overly used when it doesn't need to be.

I'm working with freeglut and C++, and have already set up the animations/event handling to use timers (using the glutTimerFunc). The glutTimerFunc, however, only allows an integer amount of milliseconds to be set – so if I want 120 FPS, the closest I can get is (int)1000/120 = 8 ms resolution, which equates to 125 FPS (I know it's a neglegible amount, but I still just want to put in an FPS limit and get exactly that FPS if I know the system can render faster).

Furthermore, using glutTimerFunc to limit the FPS never works consistently. Let's say I cap my application to 100 FPS, it usually never goes higher then 90-95 FPS. Again, I've tried to work out the time difference between rendering/calculations, but then it always overshoots the limit by 5-10 FPS (timer resolution possibly).

I suppose the best comparison here would be a game (e.g. Half Life 2) – you set your FPS cap, and it always hits that exact amount. I know I could measure the time deltas before and after I render each frame and then loop until I need to draw the next one, but this doesn't solve my 100% CPU usage issue, nor does it solve the timing resolution issue.

Is there any way I can implement an effective, cross-platform, variable frame rate limiter/cap in my application? Or, in another way, is there any cross-platform (and open source) library that implements high resolution timers and sleep functions?

Edit: I would prefer to find a solution that doesn't rely on the end user enabling VSync, as I am going to let them specify the FPS cap.

Edit #2: To all who recommend SDL (which I did end up porting my application to SDL), is there any difference between using the glutTimerFunc function to trigger a draw, or using SDL_Delay to wait between draws? The documentation for each does mention the same caveats, but I wasn't sure if one was more or less efficient then the other.

Edit #3: Basically, I'm trying to figure out if there is a (simple way) to implement an accurate FPS limiter in my application (again, like Half Life 2). If this is not possible, I will most likely switch to SDL (makes more sense to me to use a delay function rather then use glutTimerFunc to call back the rendering function every x milliseconds).