Many years ago, I used a desk striplight with a clamp. I clamped it to the back of my desk, then adjusted the angle arm so it was just above and in front of my monitor. That way, it lit the desk, didnt cast any light onto my monitor, and effectively took up no space.
It took some time to find a suitable light, and a fair amount of messing around with clamp positions and angles until I had what I wanted. Now BenQ has created a product that achieves the same result in a really neat fashion: the ScreenBar