Using the Autodialer thought experiment, we show that the Self-Sampling Assumption (SSA) is too general, and propose a revision to the assumption that limits its applicability to causally-independent observers. Under the revised assumption, the Doomsday Argument fails, and the paradoxes associated with the standard SSA are dispelled. We also consider the effects of the revised sampling assumption on tests of cosmological theories. There we find that, while we must restrict our attention to universes containing at least one observer, the total (...) number of observers predicted in each universe is irrelevant to the confirmation of a theory. (shrink)