The conventional dichotomy of “commodity” and “fiat” base monies overlooks a third possibility that shares some features of each. This third type, which I call “synthetic commodity money,” resembles fiat money in having no nonmonetary value; but it resembles commodity money in being not just contingently but absolutely scarce. I discuss some actual examples of synthetic commodity monies, and then argue that special characteristics of synthetic commodity money are such as might allow such a money, if properly designed, to supply the foundation for a monetary regime that does not require oversight by any monetary authority, yet is able to provide for a high degree of macroeconomic stability.