Mutations that cause resistance to antibiotics in bacteria often reduce growth rate by impairing some essential cellular function. This growth impairment is expected to counterselect resistant organisms from natural populations following discontinuation of antibiotic therapy. Unfortunately (for disease control) bacteria adapt and improve their growth rate, often without losing antibiotic resistance. This adaptation process was studied in mupirocin-resistant (Mup(R)) strains of Salmonella enterica. Mupirocin (Mup) is an isoleucyl-adenylate analog that inhibits the essential enzyme, isoleucyl-tRNA synthetase (IleRS). Mutations causing Mup(R) alter IleRS and reduce growth rate. Fitness is restored by any of 23 secondary IleRS amino acid substitutions, 60% of which leave resistance unaffected. Evidence that increased expression of the original mutant ileS gene (Mup(R)) also improves fitness while maintaining resistance is presented. Expression can be increased by amplification of the ileS gene (more copies) or mutations that improve the ileS promoter (more transcription). Some adapted strains show both ileS amplification and an improved promoter. This suggests a process of adaptation initiated by common amplifications and followed by later acquisition of rare point mutations. Finally, a point mutation in one copy relaxes selection and allows loss of defective ileS copies. This sequence of events is demonstrated experimentally. A better understanding of adaptation can explain why antibiotic resistance persists in bacterial populations and may help identify drugs that are least subject to this problem.