I've found that the approach of "killing" thoughts sets up an impossible and never-ending conflict that distracts from the goal of trying to fall asleep.

Instead I try to focus on something, e.g. my breath entering and existing my nose or lungs. Then, as thoughts arise I simply acknowledge them and 'let them go' returning my focus back to my breath.

It's perhaps a subtle distinction but it works much better for me than thinking about thoughts as a game of whack-a-mole.