Refurbishing of used products is increasingly being recognized as a value recovery strategy in sustainable operations. Both manufacturers and retailers engage in refurbishing. Manufacturers, to some extent, can deter other players from refurbishing through various means such as product design, intellectual property, restricting access to spare parts, and diagnostic tools. In this paper, we examine whether a manufacturer should refurbish used products himself or allow his retailer to refurbish them. While previous research has extensively examined the question of whether a manufacturer should allow an independent third-party player to refurbish used products, the question of whether a manufacturer should allow his retailer to refurbish them, to our knowledge, remains unanswered. We analyze two closed-loop supply chain structures: Model-M, where the manufacturer refurbishes used products; and Model-R, where the retailer refurbishes. In a two-period setting, new products are sold in both periods and the first-period products can be refurbished in the second period. We show that when the perceived quality of refurbished products is moderate, the manufacturer, despite forgoing profits and facing competition from refurbished products, is better off with letting the retailer refurbish used products than with refurbishing them himself. Identifying a novel mechanism through which the manufacturer benefits in Model-R is our key theoretical contribution to the closed-loop supply chain literature. Moreover, we provide some useful and interesting insights to policymakers related to customers' welfare and environment. We also analyze the performances of different models (Model-M and Model-R) in terms of the supply chain efficiency. Our results partially support some of the current policies and practices, but also shed some light on their limitations and suggest some avenues for improvement.