Multidrug combinations are increasingly important in combating the spread of antibiotic-resistance in bacterial pathogens. On a broader scale, such combinations are also important in understanding microbial ecology and evolution. Although the effects of multidrug combinations on bacterial growth have been studied extensively, relatively little is known about their impact on the differential selection between sensitive and resistant bacterial populations. Normally, the presence of a drug confers an advantage on its resistant mutants in competition with the sensitive wild-type population. Here we show, by using a direct competition assay between doxycycline-resistant and doxycycline-sensitive Escherichia coli, that this differential selection can be inverted in a hyper-antagonistic class of drug combinations. Used in such a combination, a drug can render the combined treatment selective against the drug's own resistance allele. Further, this inversion of selection seems largely insensitive to the underlying resistance mechanism and occurs, at sublethal concentrations, while maintaining inhibition of the wild type. These seemingly paradoxical results can be rationalized in terms of a simple geometric argument. Our findings demonstrate a previously unappreciated feature of the fitness landscape for the evolution of resistance and point to a trade-off between the effect of drug interactions on absolute potency and the relative competitive selection that they impose on emerging resistant populations.