Departing from Leibniz’s ontological argument, and specifically from the “possibility-complement” just as it appears in his texts, this article offers a detailed analysis of the very same concept of possibility. This is an attempt at showing its consistency in a very extreme metaphysical situation: the possibility of God without any reference to the world of possibility, contingency or eternal truths. The logic and real possibility, the merely possible, the relationship between possibility, compossibility and the Characteristic, are some of the questions dealt with in this article.