There currently exists in the literature several continuous-time one-factor models for short-term interest rates. This paper considers a wide range of these models that are nested into one general model. These models are approximated using both a discrete-time model and a model that accounts for aggregation effects over time, and are estimated by both the method of maximum likelihood and the general method of moments, for both Canadian and U.S. data. The estimation results are found to be independent of the approximation model used. However, the results are dependent on the estimation technique, more so for Canada than the United States. As an alternative check, the efficient method of moments is also employed. Hypothesis testing strongly suggests these one-factor models do not provide a good description of the evolution of Canadian short-term interest rates. In contrast, these models perform better for short-term U.S. interest rates.