This article on the epistemology of computational models stems from an analysis of the Gaïa hypothesis (GH). It begins with James Kirchner's criticisms of the central computational model of GH: Daisyworld. Among other things, the model has been criticized for being too abstract, describing fictional entities (fictive daisies on an imaginary planet) and trying to answer counterfactual (what-if) questions (how would a planet look like if life had no influence on it?). For these reasons the model has been considered not testable and therefore not legitimate in science, and in any case not very interesting since it explores non actual issues. This criticism implicitly assumes that science should only be involved in the making of models that are "actual" (by opposition to what-if) and "specific" (by opposition to abstract). I challenge both of these criticisms in this article. First by showing that although the testability-understood as the comparison of model output with empirical data-is an important procedure for explanatory models, there are plenty of models that are not testable. The fact that these are not testable (in this restricted sense) has nothing to do with their being "abstract" or "what-if" but with their being predictive models. Secondly, I argue that "abstract" and "what-if" models aim at (respectable) epistemic purposes distinct from those pursued by "actual and specific models". Abstract models are used to propose how-possibly explanation or to pursue theorizing. What-if models are used to attribute causal or explanatory power to a variable of interest. The fact that they aim at different epistemic goals entails that it may not be accurate to consider the choice between different kinds of model as a "strategy".