This paper provides an analytic treatment of the effect of differential fitness of mutants and non-mutants on the Luria-Delbruck distribution, which is used to describe the number of mutant cells obtained prior to selection during a fluctuation test experiment. It also systematizes the treatment of the case when the cultures are seeded with multiple cells. One surprising result is that differential fitness of mutants and non-mutants does not affect the mean of the distribution (though, as expected, it decreases the variance). This treatment completes the analysis of the influence of factors that affect the Luria-Delbruck distribution through mechanisms acting prior to plating. All the results that have been obtained to date are collected in a table for easy reference.