Typically, arguments against the existence of God aim to demonstrate that some property F is not instantiated, where F is typically counted among the divine attributes. In response to arguments of this form — as well as in response to perceived conflicts between divine attributes — theists face pressure to give up some pre-theoretically attractive thesis about the divine attributes. In response, theists have two options: they can try to find some flaw in the argument in question, or they can accept its conclusion and simply revise their view of God. Some examples of the second strategy are well known. We might, for instance, weaken our view of God’s power in response to perceived conflicts with the necessitation of the law of non-contradiction, or with God’s essential goodness; and we might weaken our view of God’s knowledge in response to perceived conflicts with the existence of freedom of the will, or with the existence of essentially first-personal propositions. This is always a risky strategy, for one always runs the risk of unacceptably watering down the concept of God. It would be nice to have some principled way of thinking about this topic — some principled way of deciding whether a given way of revising our views of the divine attributes is, as Peter van Inwagen nicely puts it, ‘permissible tinkering’ with the concept of God, and when it is not. Here it is very natural to — as van Inwagen and others have done — appeal to the Anselmian claim that God is the greatest possible being. This claim is often said to, in some sense, express our concept of God; and, if this is true, it seems as though examination of the notion of a greatest possible being ought to help us figure out when some claim about God contradicts the core of our conception of God. The aim of this paper to point out some difficulties which attend this initially promising strategy.