The gain in fitness during adaptation depends on the supply of beneficial mutations. Despite a good theoretical understanding of how evolution proceeds for a defined set of mutations, there is little understanding of constraints on net fitness—whether fitness will reach a limit despite ongoing selection and mutation, and if there is a limit, what determines it. Here, the dsDNA bacteriophage SP6, a virus of Salmonella, was adapted to Escherichia coli K-12. From an isolate capable of modest growth on E. coli, four lines were adapted for rapid growth by protocols differing in use of mutagen, propagation method, and duration, but using the same media, temperature, and a continual excess of the novel host. Nucleotide changes underlying those adaptations differed greatly in number and identity, but the four lines achieved similar absolute fitness at the end, an increase of more than 4000-fold phage descendants per hour. Thus, the fitness landscape allows multiple genetic paths to the same approximate fitness limit. The existence and causes of fitness limits have ramifications to genome engineering, vaccine design, and “lethal mutagenesis” treatments to cure viral infections.