Organisms often adapt to new conditions by means of beneficial mutations that become fixed in the population. Often, full adaptation requires several different mutations in the same cell, each of which may affect a different aspect of the behavior. Can one predict order in which these mutations become fixed? To address this, we experimentally studied evolution of Escherichia coli in a growth medium in which the effects of different adaptations can be easily classified as affecting growth rate or the lag-phase duration. We find that adaptations are fixed in a defined and reproducible order: first reduction of lag phase, and then an increase of the exponential growth rate. A population genetics theory explains this order, and suggests growth conditions in which the order of adaptations is reversed. We experimentally find this order reversal under the predicted conditions. This study supports a view in which the evolutionary path to adaptation in a new environment can be captured by theory and experiment.