A typical animal carcinogenicity experiment routinely analyzes approximately 10-30 tumor sites. This paper proposes using weighted adjustments by assuming that each tumor can be classified as either Class A or Class B based on prior considerations. The tumors in Class A, which are considered as more critical endpoints, are given less adjustment. Two weighted methods of adjustments are presented: the weighted p adjustment and weighted adjustment. The power to detect a dose effect increases if a treatment-dependent tumor is analyzed as in Class A tumors, and the power decreases if it is analyzed as in Class B tumors. A data set from an National Toxicology Program (NTP) two-year animal carcinogenicity experiment with thirteen tumor types/sites observed in male mice was analyzed using the un-weighted and weighted methods. The un-weighted adjustment concluded that there was no statistically significant dose-related trend. Using the FDA classification scheme for the weighted adjustment analyses, two rare tumors (with background rates of 1% or less) were analyzed as Class A tumors and eleven common tumors (with background rates higher than 1%) as Class B. Both weighted analyses showed a significant dose-related trend for one rare tumor.