Antibiotic resistance is a growing concern to public health. New treatment strategies may alleviate the situation by slowing down the evolution of resistance. Here, we evaluated sequential treatment protocols using two fully independent laboratory-controlled evolution experiments with the human pathogen Pseudomonas aeruginosa PA14 and two pairs of clinically relevant antibiotics (doripenem/ciprofloxacin and cefsulodin/gentamicin). Our results consistently show that the sequential application of two antibiotics decelerates resistance evolution relative to monotherapy. Sequential treatment enhanced population extinction although we applied antibiotics at sublethal dosage. In both experiments, we identified an order effect of the antibiotics used in the sequential protocol, leading to significant variation in the long-term efficacy of the tested protocols. These variations appear to be caused by asymmetric evolutionary constraints, whereby adaptation to one drug slowed down adaptation to the other drug, but not vice versa. An understanding of such asymmetric constraints may help future development of evolutionary robust treatments against infectious disease.