Thanks, k99 and Vitalik, that helps clear it up. I've put "On Transaction Fees, And The Fallacy of Market-Based Solutions" on my to-think-about-deeply list.
I'm curious about this, though:
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If my contract needs more than 16 computational steps to execute, then other people CAN send transactions to it to intentionally bankrupt it? That is what I was worrying about when I said "publish the attacker's transaction and take the fee but ignore any other effects of the transaction, but you'd have to be careful to design THAT mechanism so it couldn't be abused."