This paper develops an adverse selection model of mixed bundling. By packaging its product with a competitively produced good unrelated in demand, a monopolist can induce self-selection of different types of consumers into buyers of the bundle and of the separate components. Private and social optimality conditions of bundling are derived. The effect on prices and welfare depends on the demand elasticities for the bundled and unbundled good. By overcoming information asymmetries, bundling may raise welfare if it leads to a sufficiently strong expansion of the market. It is possible that prices to all buyers rise; in this case welfare definitely falls if the bundle is introduced.