Though the very task of modeling God implies that the reality of God is to some degree unknowable, there are a variety of positions one may take concerning the degree to which one has epistemic access to God. If our models of God are too influenced by subjectivity, it makes no sense to test them against each other in rational competition. In this essay, I define four possible positions that may underlie the task of God-modeling: mysteriosophy, theopoetics, critical realism, and fallibilism. Of these four, I propose that fallibilism is the most appropriate method for constructing models of God. Fallibilism simultaneously assumes that our models are able to refer to a divine reality, and yet always with a tentative stance, as absolute confirmation or universal consensus concerning them will almost certainly never be obtained. Models of God can engage in rational competition, but a final decision will probably be delayed indefinitely. This paper was delivered during the APA Pacific 2007 Mini-Conference on Models of God.