Replicate lineages of the bacteriophage phiX 174 adapted to growth at high temperature on either of two hosts exhibited high rates of identical, independent substitutions. Typically, a dozen or more substitutions accumulated in the 5.4-kilobase genome during propagation. Across the entire data set of nine lineages, 119 independent substitutions occurred at 68 nucleotide sites. Over half of these substitutions, accounting for one third of the sites, were identical with substitutions in other lineages. Some convergent substitutions were specific to the host used for phage propagation, but others occurred across both hosts. Continued adaptation of an evolved phage at high temperature, but on the other host, led to additional changes that included reversions of previous substitutions. Phylogenetic reconstruction using the complete genome sequence not only failed to recover the correct evolutionary history because of these convergent changes, but the true history was rejected as being a significantly inferior fit to the data. Replicate lineages subjected to similar environmental challenges showed similar rates of substitution and similar rates of fitness improvement across corresponding times of adaptation. Substitution rates and fitness improvements were higher during the initial period of adaptation than during a later period, except when the host was changed.