Firstly rather accurate approximations to the p value functions of the common Standard CUSUM test and the OLS-based CUSUM test for structural change are derived. Secondly alternative boundaries for both tests are suggested and their properties are examined by simulation of expected p values. It turns out that the power of the OLS-based CUSUM test for early and late structural changes can be improved, whereas this weakness of the Standard CUSUM test cannot be repaired by the new boundaries. / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"