In this article I criticize the non-consequentialist Weighted Lottery (WL) solution to the choice between saving a smaller or a larger group of people. WL aims to avoid what non-consequentialists see as consequentialism's unfair aggregation by giving equal consideration to each individual's claim to be rescued. In so doing, I argue, WL runs into another common objection to consequentialism: it is excessively demanding. WL links the right action with the outcome of a fairly weighted lottery, which means that an agent (...) can only act rightly if s/he has actually run the lottery. In many actual cases, this involves epistemic demands that can be almost impossible to meet. I argue that plausible moral principles cannot make such extreme epistemic demands. (shrink)