Scientists seek to learn about targets of interest by representing them with models. This supposes that we have an account of how models represent. Typically, such accounts have been concerned with real-world targets or, more precisely, actual targets. However, some models appear to not have actual targets (Weisberg 2013, sec. 7). This raises a puzzle: how could models represent non-actual targets? This paper aims to answer that question using Frigg and Nguyen’s (e.g. 2016) denotation-exemplification-keying up-imputation (DEKI) account of scientific representation. The argument proceeds in two steps. First, illustrating with the case of the perpetual motion machine (Feynman, Leighton, and Sands 2010, ch. 46), I argue that models with non-actual targets targets do not, contrary to what we might believe, necessarily fail to denote. Denotation failure implies failure to be an epistemic representation. This is at odds with a naturalistic interpretation of scientific practice. My proposal, which avoids postulating ontologically problematic entities (e.g nonexistent objects), is that these models simply denote properties of the actual world. Second, I argue that that the properties we key up and impute with these models are modal properties of actual targets. I illustrate with a case from economics (Arrow and Debreu 1954) and show that the general equilibrium model exemplifies the properties a system needs to have in order for the equilibrium to exist. Then, modal properties are imputed on actual economic systems. This accounts for how, within the DEKI framework, models with ostensibly non-actual targets may represent.