Jackpots of mutations are the bane of transgenic mutation assays, for they can produce large mutant frequencies even in the absence of a mutagen. A jackpot is a large number of mutants that arose from a single mutation. They arise when there is a clonal expansion of a mutated cell. Jackpots as large as 1000 mutants/100 000 plaques have been observed, a mutant frequency of 1%. Such a jackpot can swamp not only the spontaneous mutant frequency but even the mutant frequency induced by potent mutagens, which are rarely .0.2% with even the most potent mutagens and are usually much lower (Hoorn et al., 1993; Tao et al., 1993; Morrison and Ashby, 1994; Douglas et al., 1995; Mirsalis et al., 1995; Skopek et al., 1995; Cosentino and Heddle, 1999). Very large jackpots are not normally a problem, for they are statistical outliers and can be discarded legitimately by standard statistical tests. These large jackpots arise when a mutation occurs early in development in one of the progenitor cells for one or more tissues. The normal growth of the organism is by clonal expansion of the cells present during the preceding stage. Accordingly, mutations arising at an early stage of development produce a large number of mutant cells, i.e. a jackpot, when these are recovered together. Smaller jackpots, from mutations arising later in development, are harder to identify and are, thus, more problematic. Numerous proposals have been made to deal with this problem including complex statistical analysis and the sequencing of each and every mutant (de Boer et al., 1996; Knoll et al., 1996). There is a simple method of dealing with the data without such extraordinary efforts. In fact, current methods over-compensate for jackpots and thus distort both the mutant frequency and the mutation spectrum. The transgenes present in the MutaTM Mouse and the Big BlueTM Mouse are bacterial genes embedded in a recoverable λ vector (Gossen et al., 1989; Kohler et al., 1991). They lack mammalian promoters or polyadenylation sites and are, presumably, unexpressed and unimportant to the mouse. Theoretically and practically they are genetically neutral, providing neither benefit nor harm to the cell containing them (Tao et al., 1993; Tao and Heddle, 1994; Cosentino and Heddle, 1996). This being the case, a cell containing a mutated transgene is neither more nor less likely to expand than any cell without such a mutation. In a large number of animals, therefore, clonal expansion will have no effect on the average mutant frequency: expansions of the numerous non-mutants will each tend to decrease the mutant frequency somewhat while expansions of the rare mutants will each tend to increase the mutant frequency to a larger extent (Figure 1). Nevertheless,