Despite some recent criticisms, the conventional radial distance function, which treats undesirable by-products as either frontier shifters or inputs, remains a popular go-to formulation of polluting production processes among practitioners. This unfading popularity is arguably driven by the ability of radial distance functions, unlike alternative directional distance functions, to allow for unit-free multiplicative changes in arguments as well as, by implicitly postulating the radial direction, to free researchers from the dilemma of having to explicitly choose the directional vector. In this paper, we offer a generalization of the standard radial distance function to polluting technologies that can accommodate undesirable by-products in a more economically meaningful way. Specifically, we propose modeling undesirable outputs via a hedonic output index, which is meant to ensure that pollutants are treated as outputs, as opposed to inputs or theoretically unregulated frontier shifters, while also recognizing their undesirable nature. By using a radial input distance function generalized to encompass an (unobservable) hedonic output index of desirable and undesirable outputs, we are able to meaningfully describe relationships between different products (including the complementarity of desirable and undesirable outputs) within producible output sets as well as to represent technically feasible polluting production possibilities given inputs. An empirical application of our methodology to the case of Dutch dairy farms in 2001–2009 demonstrates the complexity of interactions between outputs, thereby attesting to the value of more elaborate representations of production possibilities.