AbstractThis paper incorporates fairness constraints into the classic single-unit reduced-form implementation problem (Border in Economet J Econ Soc, 59(4):1175–1187, 1991, Econ Theory 31(1):167–181, 2007; Che et al. in Econometrica 81(6): 2487–2520, 2013; Manelli and Vincent in Econometrica, 78(6):1905–1938, 2010) with two agents. To do so, I use a new approach that utilizes the results from Kellerer (Math Ann 144(4):323–344, 1961) and Gutmann et al. (Ann Prob 19:1781–1797, 1991). Under realistic assumptions on the constraints, the conditions are transparent and can be verified in polynomial time.