In Posterior Analytics II 16-17, Aristotle seems to claim that there cannot be more than one explanans of the same scientific explanandum. However, this seems to be true only for “primary-universal” demonstrations, in which the major term belongs to the minor “in itself” and the middle term is coextensive with the extremes. If so, several explananda we would like to admit as truly scientific would be out of the scope of an Aristotelian science. The secondary literature has identified a second problem in II 16-17: the middle term of a demonstration is sometimes taken as the definition of the minor term (the subject), other times as the definition (or the causal part of the definition) of the major (the demonstrable attribute). I shall argue that Aristotle’s solution to the first problem involves showing that certain problematic attributes, which appear to admit more than one explanation, actually fall into the privileged scenario of primary-universal demonstrations. In addition, his solution suggests a conciliatory way-out to our second problem (or so I shall argue): the existence of an attribute as a definable unity depends on its subject having the essence it has, which suggests that both the essence of subjects and the essence of demonstrable attributes can play explanatory roles in demonstrations.