We investigate whether a market served by a multiproduct monopolistic seller can be segmented in a way that benefits all consumers and the seller. The seller can offer a different product menu in each market segment, combining second- and third-degree price discrimination. We show that markets for which profit maximization leads to inefficiency can, generically, be segmented into two market segments in a way that increases the surplus of all consumers weakly and of some consumers and the seller strictly. Our constructive proof is based on deriving implications of binding incentive compatibility constraints when profit maximization implies inefficiency.