In this paper we provide analytical and Monte Carlo evidence that Chow and Predictive tests can be consistent against alternatives that allow structural change to occur at either end of the sample. Attention is restricted to linear regression models that may have a break in the intercept. The results are based on a novel reparameterization of the actual and potential break point locations. Standard methods parameterize both of these locations as fixed fractions of the sample size. We parameterize these locations as more general integer valued functions. Power at the ends of the sample is evaluated by letting both locations, as a percentage of the sample size, converge to zero or one. We find that for a potential break point function, the tests are consistent against alternatives that converge to zero or one at sufficiently slow rates and are inconsistent against alternatives that converge sufficiently quickly. Monte Carlo evidence supports the theory though large samples are sometimes needed for reasonable power.