Leibniz stresses the incompleteness of previous versions of the ontological argument: they only show that ‘If God is possible, God exists.’ To be unconditionally conclusive, the argument must be formulated as follows: 1. If God is possible, God exists; 2. God is possible; 3. Therefore, God exists. The first part of this chapter discusses Leibniz’s attempts to support the first premise by defining God as the Ens perfectissimum, and by arguing, in turn, that a most perfect being implies necessary existence. The relationship between perfection and existence and Leibniz’s modal version of the argument are examined in detail. The second part turns to Leibniz’s attempts to support the second premise. His favourite strategy for proving God’s possibility, namely his arguments for the ‘pure positivity’ of the Ens perfectissimum, is outlined and evaluated. The chapter then focuses on his a posteriori approach based on a version of the cosmological argument, and on his proposal of a weaker strategy based on the presumption of possibility. The overall conclusion is that, for Leibniz, the only true objection to the ontological argument is the issue of God’s possibility. His arguments for God’s possibility face, however, significant objections which challenge his claim to have succeeded in completing the argument.