The primary impediment to formulating a general theory for adaptive evolution has been the unknown distribution of fitness effects for new beneficial mutations. By applying extreme value theory, Gillespie circumvented this issue in his mutational landscape model for the adaptation of DNA sequences, and Orr recently extended Gillespie's model, generating testable predictions regarding the course of adaptive evolution. Here we provide the first empirical examination of this model, using a single-stranded DNA bacteriophage related to phiX174, and find that our data are consistent with Orr's predictions, provided that the model is adjusted to incorporate mutation bias. Orr's work suggests that there may be generalities in adaptive molecular evolution that transcend the biological details of a system, but we show that for the model to be useful as a predictive or inferential tool, some adjustments for the biology of the system will be necessary.