Mascara

I've been trying to use up my make-up recently and have run into a problem with mascara removal. What do all you mascara-wearers out there do to remove it effectively? I have eye make-up remover but then the mascara collects in black smudges under my eyes. It's fine if I only wear it once a week or something but really not good for every day. I hate clawing at my eyes and I hate going around looking like I was in a fist fight. Does everyone do this? Am I missing something? Tell me!