Abstract: Physicalism is the claim that the physical facts are sufficient for all the actual facts. But what is the pertinent relation of sufficiency? Standardly, it is explained either in terms of supervenience, or of logical entailment. I characterize a different relation, sufficiency ceteris absentibus , or other things being absent. The idea is that some facts give rise to others only as long as potentially interfering 'blockers' are absent. I argue that if physicalism is to be strong and yet philosophically defensible, it ought to be understood as the claim that the physical facts are sufficient for all actual facts, other things being absent. This claim captures the intuition that nothing over and above physical facts is needed to give rise to the world in its richness and variety. Yet it does not fall victim to the most substantial threat to physicalism, the Conceivability Argument. This argument tries to establish that physical facts cannot account for facts about conscious experience. Extant physicalist responses deny either the intuitively compelling premise that so-called 'zombies' are conceivable, or the philosophically attractive premise that conceivability entails possibility. My response has the advantage of being consistent with both these claims. Even though it is possible that a physical duplicate of me lacks conscious experience, in the absence of blockers physical facts may be sufficient for such experience.