What if you are making something and you need to countersink the screws into a part that will be finished? How do you cut the countersinks cleanly and have them a perfect fit for the screws you will use? Here’s a method that I’ve used time and time again.
Basically, I use the screw itself as the countersink. I just cut some grooves in the underside of the head with a file:

Cut the threads off completely:

And use it mounted on a driver bit chucked in a drill. The process is fairly slow to avoid burning, but you probably won’t need to use this often.

It cuts a precise, clean countersink that is exactly the right size for the screw:

There are screws that have ribs under the head and these will work as well, just cut off the threads.

I made a video demonstrating how it works:

It’s important to note that this is for special situations and is not meant to replace a regular countersink bit for most operations.