Thread.Sleep(1) waits approx. 15 ms in stead of 1

Ever noticed how the time Thread.Sleep(int x) waits is not equal to x? I just noticed it happening with 2 threads with different values for the sleep, yet they were running just as quick.
After some research I discovered that the .Net runtime and Windows map this to a lower resolution in time, due to the way they handle threads. According to some sites it is 15.6 ms.
This means that any x between 1 and 15 will have your thread wait 15.6 ms (give or take, as it might be that your thread has to wait a bit more because of other calculations your CPU is processing). Any value between 16 and 31 will have your thread wait 2 x 15.6 ms (i.e. 31.2 ms) etc. The documentation also states that Thread.Sleep(int x) does not wait exactly x milliseconds, but rather "at least" x milliseconds.
For me, this is not a problem, I have just set the thread that was supposed to go slower to a different value, to make sure it actually runs slower. But just out of curiosity I have done some more research into how to solve it if you really want to have your thread sleep for a more precise period of time.
It seems the MultiMedia API's can help with that. I have tested the following code and it allowed me to set the sleep to a millisecond precisely.

[DllImport("winmm.dll")]internal static extern uint timeBeginPeriod(uint period);

[DllImport("winmm.dll")]
internal static extern uint timeEndPeriod(uint period);


{

Thread.Sleep(1); // waits roughly 15ms
Thread.Sleep(2); // waits roughly 15ms
Thread.Sleep(3); // waits roughly 15ms

timeBeginPeriod(1);

Thread.Sleep(1); // waits just over 1 ms
Thread.Sleep(2); // waits just over 2 ms
Thread.Sleep(3); // waits just over 3 ms

timeEndPeriod(1);

Thread.Sleep(1); // waits roughly 15ms
Thread.Sleep(2); // waits roughly 15ms
Thread.Sleep(3); // waits roughly 15ms

}

(this code was found here, posted by Per, so all credits go to him for this idea)