Among existing classifier combination rules the most widely used are Sum, Product and Vote. Although Product is more directly related to the compound class posterior probability, it does not perform well. Sum, which is derived under restricting assumptions, outperforms product, especially if the class a posteriori probability estimates are subject to high levels of noise.We establish the cause of Product's degraded performance and propose a method to improve it. Tests on real and synthetic data demonstrate that the modified Product has a number of advantages in relation to other rules that we experiment with.