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So, you're painting your last piece - a bell housing. You're down to your last half-can of Old Ford Blue. You jerk the lid off the can, snapping off the push button flush with the top of the can.
How to get the button stub out of the can so you can re-use another button from another can? Grab a drill bit the same diameter as the button stem - don't chuck it in your drill, though. Just spin it into the broken stem until it "bites" into the plastic and pull it out.
Be careful not to put too much pressure on the bit while your face is over the can. Don't ask me how I know this....