Abstract The conventional wisdom holds that the short-run demand for money is unstable. This paper challenges the conventional view by finding a stable demand for M1 in U.S. data from 1959 through 1993. The approach follows previous work in interpreting long-run money demand as a cointegrating relation, and it uses Goldfeld's partial-adjustment model to interpret short-run dynamics. The key innovation is the choice of the interest rate in the money demand function. Most previous work uses a short-term market rate, but this paper uses the average return on “near monies”—the savings accounts and money market mutual funds that are close substitutes for M1. This choice helps rationalize the behavior of money demand; in particular, the increase in the volatility of velocity after 1980 is explained by increased volatility in the returns on near monies.