In this paper the scenario in which low credit risk banks with liquidity shortages leave the market is studied. In this case, the interest rate is too high when it is compared to an alternative source of funding because banks are not able to set it based on the risk of its counterparty due to asymmetric information. Given this, two types of contracts for interbank lending are proposed with the purpose of encouraging banks to trade among them to smooth out liquidity shock. Such contracts differ in both the interest rates and also a mandatory deposit: whenever a bank meets the required deposit the interest rate of its loans will be low, otherwise the interest rate will be high.