Experimental evolution studies have provided key insights into the fundamental mechanisms of evolution. One striking observation is that parallel and convergent evolution during laboratory evolution can be surprisingly common. However, these experiments are typically performed with well-mixed cultures and large effective population sizes, while pathogenic microbes typically experience strong bottlenecks during infection or drug treatment. Yet, our knowledge about adaptation in very small populations, where selection strength and mutation supplies are limited, is scant. In this study, wild-type and mutator strains of the bacterium Escherichia coli were evolved for about 100 generations towards increased resistance to the β-lactam antibiotic cefotaxime in millifluidic droplets of 0.5 µL and effective population size of approximately 27,000 cells. The small effective population size limited the adaptive potential of wild-type populations, where adaptation was limited to inactivating mutations, which caused the increased production of outer-membrane vesicles, leading to modest fitness increases. In contrast, mutator clones with an average of ~30-fold higher mutation rate adapted much faster by acquiring both inactivating mutations of an outer-membrane porin and particularly inactivating and gain-of-function mutations, causing the upregulation or activation of a common efflux pump, respectively. Our results demonstrate how in very small populations, clonal interference and mutation bias together affect the choice of adaptive trajectories by mediating the balance between high-rate and large-benefit mutations.