It is commonly argued that an undesirable feature of a theoretical or phenomenological model is that salient observables are sensitive to values of parameters in the model. But in what sense is it undesirable to have such ‘fine-tuning’ of observables? In this paper, we argue that the fine-tuning can be interpreted as a shortcoming of the explanatory capacity of the model: in particular it signals a lack of a particular type of explanatory depth. The aspect of depth that we probe (...) relates most closely to a lack of sensitivity to changes in parameters associated with such models. In support of this argument, we develop a schema—for models that arise broadly in physical settings—that quantitatively relates fine-tuning of observables to a lack of depth of explanations based on these models. We apply our schema in two different settings in which, within each setting, we compare the depth of two competing explanations. The first setting involves explanations for the Euclidean nature of spatial slices of the universe today: in particular, we compare an explanation provided by the big-bang model of the early 1970s with an explanation provided by a general model of cosmic inflation. The second setting has a more phenomenological character, where the goal is to infer from a limited sequence of data points, using maximum entropy techniques, the underlying probability distribution from which these data are drawn. In both of these settings we find that our analysis favors the model that intuitively provides the deeper explanation of the observable of interest. We thus provide an account that relates two ‘theoretical virtues’ of models used broadly in physical settings—namely, a lack of fine-tuning and explanatory depth—and argue that finely tuned models sacrifice explanatory depth. (shrink)