jfain, have you ever seen one of those bagel cutters? Imagine turning one of them on their side.

You're not squishing the tomatoes. Basically you're using the plastic lids to stabalize the tomatoes or olives while you cut through them with a knife.

I find I can cut an entire layer of them this way in about the same time it takes to halve two of them working one at a time.

Hopefully, this sketch will help.

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cut here