Although both genotypes with elevated mutation rate (mutators) and mobilization of insertion sequence (IS) elements have substantial impact on genome diversification, their potential interactions are unknown. Moreover, the evolutionary forces driving gradual accumulation of these elements are unclear: Do these elements spread in an initially transposon-free bacterial genome as they enable rapid adaptive evolution? To address these issues, we inserted an active IS1 element into a reduced Escherichia coli genome devoid of all other mobile DNA. Evolutionary laboratory experiments revealed that IS elements increase mutational supply and occasionally generate variants with especially large phenotypic effects. However, their impact on adaptive evolution is small compared with mismatch repair mutator alleles, and hence, the latter impede the spread of IS-carrying strains. Given their ubiquity in natural populations, such mutator alleles could limit early phase of IS element evolution in a new bacterial host. More generally, our work demonstrates the existence of an evolutionary conflict between mutation-promoting mechanisms.