We examine several discrete-time versions of the Cox, Ingersoll and Ross (CIR) model for the term structure, in which the short rate is subject to discrete shifts. Our empirical analysis suggests that careful consideration of which parameters of the short-term interest rate equation that are allowed to be switched is crucial. Ignoring this issue may result in a parameterization that produces no improvement (in terms of bond pricing) relative to the standard CIR model, even when there are clear breaks in the data.