We develop a theoretical model in which firms may choose multiple banking relationships to reduce the risk that financing will be denied by "relationship banks" should the latter experience liquidity problems and refuse to roll over lines of credit. The inability to refinance from relationship banks signals unfavorable information about the quality of the firm’s project, which may also prevent the firm from obtaining credit from other banks. We show that if this "lemons" problem is severe, then it is optimal to establish a relationship with more than one bank in spite of higher transaction costs; if it is mild, a single banking relationship is optimal. We find that the severity of the lemons problem depends directly on the inefficiency of bankruptcy procedures and inversely on the "fragility" of the banking system. The paper concludes with a comparison of bank-firm relationships in Italy and the U.S., characterized respectively by multiple and single banking. We present evidence that bankruptcy costs are significantly higher and banks less fragile in Italy than in the U.S., suggesting that the factors identified by the theoretical model are relevant in practice.