Conventional wisdom holds that the best way to treat infection with antibiotics is to 'hit early and hit hard'. A favoured strategy is to deploy two antibiotics that produce a stronger effect in combination than if either drug were used alone. But are such synergistic combinations necessarily optimal? We combine mathematical modelling, evolution experiments, whole genome sequencing and genetic manipulation of a resistance mechanism to demonstrate that deploying synergistic antibiotics can, in practice, be the worst strategy if bacterial clearance is not achieved after the first treatment phase. As treatment proceeds, it is only to be expected that the strength of antibiotic synergy will diminish as the frequency of drug-resistant bacteria increases. Indeed, antibiotic efficacy decays exponentially in our five-day evolution experiments. However, as the theory of competitive release predicts, drug-resistant bacteria replicate fastest when their drug-susceptible competitors are eliminated by overly-aggressive treatment. Here, synergy exerts such strong selection for resistance that an antagonism consistently emerges by day 1 and the initially most aggressive treatment produces the greatest bacterial load, a fortiori greater than if just one drug were given. Whole genome sequencing reveals that such rapid evolution is the result of the amplification of a genomic region containing four drug-resistance mechanisms, including the acrAB efflux operon. When this operon is deleted in genetically manipulated mutants and the evolution experiment repeated, antagonism fails to emerge in five days and antibiotic synergy is maintained for longer. We therefore conclude that unless super-inhibitory doses are achieved and maintained until the pathogen is successfully cleared, synergistic antibiotics can have the opposite effect to that intended by helping to increase pathogen load where, and when, the drugs are found at sub-inhibitory concentrations.