The primary objective of closed-loop supply chains (CLSC) is to improve the maximum economic benefit from end-of-use products. Nevertheless, the literature within this stream of research advocates that closing the loop also helps to mitigate the undesirable environmental footprint of supply chains. Therefore, closed-loop supply chains are assumed to be sustainable supply chains almost by definition. In this paper we analyse if and when this assumption holds. We illustrate our findings based on the Electric and Electronic Equipment (EEE) supply chain. For all phases of the supply chain, i.e. manufacturing, usage, transportation and end-of-life activities, we assess the magnitude of the environmental impacts, based on a single environmental metric, namely the Cumulative Energy Demand (CED). Given the environmental hot-spots in the Electric and Electronic Equipment supply chain, we propose useful extensions for existing CLSC optimisation models to ensure that closed-loop supply chains are at the same time sustainable supply chains.