Leftover fish; tasty lunch or food poisoning waiting to happen?

I bought Alaskan halibut yesterday at the Pike Place market. We grilled it for dinner. I left enough for lunch leftovers. My dining partner was appalled. "You don't eat leftover fish!" I've always eaten leftover fish. It hasn't happened recently, because I usually balk at the price and don't buy enough and we don't have any leftover. You gotta figure that the leftover fish bought at the Market yesterday is fresher than just about anything you'd get anywhere else. Any other thoughts? Office lunchtime poll is entirely in my favor, but the real proof will be in how I feel an hour from now.