Despite widespread resistance to many important antibiotics, the factors that govern the emergence and prevalence of antibiotic-resistant bacteria are still unclear. When exposed to antibiotic gradients in soft agar plates measuring as little as 1.25 × 11 cm we found that Escherichia coli rapidly became resistant to representatives from every class of antibiotics active against Gram-negative bacteria. Evolution kinetics were independent of the frequency of spontaneous mutations that confer antibiotic resistance or antibiotic dose-response curves, and were only loosely correlated to maximal antibiotic concentrations. Instead, rapid evolution required unrealized mutations that could markedly decrease antibiotic susceptibility. When bacteria could not evolve through these "high-impact" mutations, populations frequently bottlenecked, reducing the number of cells from which mutants could arise and prolonging evolution times. This effect was independent of the antibiotic's mechanism of action, and may affect the evolution of antibiotic resistance in clinical settings.