Good explanations can be distinguished from bad ones in different ways, for instance by how much of the available information they can explain (i.e., maximise the likelihood of) the available data. Here, we consider two different components of likelihood: descriptiveness (the likelihood of the individual data points) and co-explanation (the likelihood of the specific subset of data under consideration). We consider whether people prefer explanations that are high in descriptiveness vs. coexplanation. Moreover, we consider whether people who endorse conspiracy theories prefer explanations for either quality. In a medical diagnosis task, participants make binary choices between two fictional disease variants: one higher in descriptiveness versus another higher in co-explanation. Overall, participants displayed a weak preference for descriptiveness. This preference, however, did not vary across increasing levels of descriptiveness. Moreover, such preferences were unrelated to conspiracy mentality. Thus, both explanatory virtues may play a role in the appeal of likely explanations.