Short-term interest rate processes determine the term structure of interest rates in an arbitrage-free market and are central to the valuation of interest rate derivatives. We obtain parameter estimates and compare the empirical fit of alternative one-factor continuous-time processes for the South African short-term interest rate (and hence of arbitrage-free term structure models) using Gaussian estimation methods. We find support only for diffusions where the interest rate volatility is moderately sensitive to the level of the interest rate. Other common models with restrictions that either preclude this effect, or restrict it to be too high, do not fit the data. Differences in the specification of the drift function have no evident effect on model performance.