We revisit the classic problem of a seller (e.g. firm) who is privately informed about her asset and needs to raise funds from uninformed buyers (e.g. investors) by issuing securities backed by her asset cash flows. In our setting, buyers post menus of contracts to screen the seller, but the seller cannot commit to accept contracts from only one buyer, i.e., markets are non-exclusive. We show that an equilibrium of this screening game always exists, it is unique and features semi-pooling allocations for a wide range of parameters. In equilibrium, the seller tranches her asset cash flows into a debt security (senior tranche) and a levered-equity security (junior tranche). Whereas the seller of a high quality asset only issues her senior tranche, the seller of a low quality asset issues both tranches but to distinct buyers. Consistent with this, whereas the senior tranche is priced at pooling valuation, the junior tranche is priced at low valuation. Our theory's positive predictions are consistent with recent empirical evidence on issuance and pricing of mortgage-backed securities, and we analyze its normative implications within the context of recent reforms aimed at enhancing transparency of financial markets.