I present an environment for which both outside and inside money are essential as means of payment. The key model feature is that there is imperfect monitoring of issuers of inside money. I use a random-matching model of money where some agents have private trading histories and others have trading histories that can be publicly observed only after a lag. I show via an example that for lags that are neither too long nor too short, there exist allocations that use both types of money that cannot be duplicated when only one type is used. Inside money provides liquidity that increases the frequency of trades, but incentive constraints restrict the amount of output that can be traded. Outside money is immune to such constraints and can trade for higher levels of output.