Imagination is analysed by contemporary philosophers of mind in order to discover its features and its place in our cognitive architecture. More precisely, the debate has given birth to two competing approaches: simulationism and single-code theory. However, a third, intermediary view, is possible, as Mulligan’s proposal suggests. In this paper I propose a certain type of simulationism, namely a conception of imagination based on a homomorphic functional simulation. Inspired by Mulligan’s position, I will argue that this type of simulationism is in fact neutral with respect to the disagreement between classical simulationists and single-code theorists. It can even be regarded as the common ground of these approaches.