Using the monetary model developed in Sissoko (2007), where the general equilibrium assumption that every agent buys and sells simultaneously is relaxed, we observe that in this environment fiat money can implement a Pareto optimum only if taxes are type-specific. We then consider intermediated money by assuming that financial intermediaries whose liabilities circulate as money have an important identifying characteristic: they are widely viewed as default-free. The paper demonstrates that default-free intermediaries who issue credit lines to consumers can resolve the monetary problem and make it possible for the economy to reach a Pareto optimum. We argue that our idealized concept of financial intermediation is a starting point for studying the monetary use of credit.