But I don't. I want to move the mouse around a bit without leaving the keyboard, in a very fast and very efficient way. It's okay even if the mouse control isn't very fine-grained, as it's mostly just to move the cursor from one window to another, in order to activate a window.
Enter keynav. Problem solved.
It's available for many distributions of Linux. It's fast and easy. I can "throw" the cursor to the right side of the screen with just a
ctrl-; l ;. And that helps me keep my hands at the keyboard.