This paper considers regression models which are mis-specified through the omission of relevant regressors, and investigates some aspects of the power properties of the Goldfeld-Quandt test for homoscedasticity of the error variance in such cases. Attention focusses not on the full power function of the test, but on the locus of powers that emerges when, for a given departure from the null, different numbers of central observations are omitted in the construction of the test statistic. A well known rule of thumb regarding the optimal number of such observations is found to be questionable, whether the model is mis-specified or not. The form of the regressor data, and the sample size, are found to be important in governing these features of the test.