If whales were fish, their behaviour would differ from what it actually is. If whales were fish, their behaviour would be just as it actually is. Those sound like genuine alternatives. Yet, since whales are by nature mammals, they presumably could not have been fish; that would be contrary to their nature. Thus both conditionals are counterpossibles, counterfactual conditionals with impossible antecedents. Semantic orthodoxy makes all counterpossibles true. So the two conditionals were true, and not mutually exclusive after all. Is orthodoxy about counterpossibles correct? The problem is not just how best to tidy up an unimportant little corner of the logic and semantics of counterfactuals. It has significant theoretical and methodological ramifications in several directions. This paper defends orthodoxy against recent objections, and explains recalcitrantly unorthodox appearances by our pre-reflective reliance on a fallible heuristic in assessing conditionals.