Sparse data is a difficulty in the analysis of animal carcinogenicity data: it is difficult to detect effects when the background tumor rates are low. The widely used "Haseman rule" and its variants provide more power to tests with low background rates, while maintaining a degree of control over the global false positive rate. In this article we explore the use of these rules, finding global error rates that are unacceptably high for many animal carcinogenicity studies. We provide alternative weighting methods that correct the deficiencies of the Haseman rule, and apply them to carcinogenicity data from a pharmaceutical company.