One strategy that scientists use to understand targets of interest is by representing them with models. Understanding the world by representing it supposes we have an account of what it is for models to represent their targets. Typically, accounts of that relation have been concerned with real-world targets or, more precisely, actual targets. Actual targets are those that exist in the actual world. However, as Weisberg (2013, sec. 7) pointed out in his discussion of hypothetical modelling, some models appear to not have actual targets in that sense. For instance, a model of a perpetual-motion machine or a model of xDNA represent, respectively, something that is either nomologically impossible or contingently non-actual. This suggests that models may also have (im)possible targets. But how could models represent (im)possible targets and afford understanding? This paper discusses the representation of (im)possible targets in the context of Frigg and Nguyen’s (e.g. 2016; 2018; 2019) denotation-exemplification-keying up-imputation (DEKI) account of scientific representation. The main goal of the paper is to show how models with ostensibly (im)possible targets satisfy, contrary to what Frigg and Nguyen hold, the DEKI conditions. The argument proceeds in two steps. Firstly, I argue that it is incorrect to consider that models such as those that Weisberg (2013) discusses fail to denote a target. Secondly, I show in more detail how DEKI already has the resources to account for models with ostensibly (im)possible targets.