Thought about God in the Western monotheistic traditions is drawn in two conflicting directions: theistic faith demands that we offer some description of God, but there are also powerful theological intuitions suggesting that none of our creaturely concepts could properly apply to God. One traditional solution to this problem is to assert that we speak analogically of God: that God is not, e.g., wise in the same sense as any creature, but instead has something similar to wisdom. But William Alston and others have argued that analogical claims must be reducible to non-analogical ones or else they will be too empty of propositional content to support a substantial religious faith. I argue that we must understand analogical speech about God to consist not in simple similarity claims, but instead in claims which either construct, or are based on, analogical models of God. Accepting a model involves not only accepting particular similarity claims, but also taking up a particular cognitive and practical stance towards the modeled object. This enables an irreducibly analogical theology to be more contentful than Alston supposes. On the approach I propose for interpreting religious language, believers accept certain models of God in a certain way, and take certain crucial models to be both irreducible and irreplaceable. I demonstrate that is possible for such a theology to be coherent, realist in purport, and sufficiently contentful to support a robust religious faith and practice, even if one takes the fairly radical position that all true, positive ascriptions of intrinsic properties to God are irreducibly analogical.