Here, a model allowing covarion-like evolution of DNA sequences is introduced. In contrast to standard representation of the distribution of evolutionary rates, this model allows the site-specific rate to vary between lineages. This is achieved by adding as few as two parameters to the widely used among-site rate variation model, namely, (1) the proportion of sites undergoing rate changes and (2) the rate of rate change. This model is implemented in the likelihood framework, allowing parameter estimation, comparison of models, and tree reconstruction. An application to ribosomal RNA sequences suggests that covarions (i.e., site-specific rate changes) play an important role in the evolution of these molecules. Neglecting them results in a severe underestimate of the variance of rates across sites. It has, however, little influence on the estimation of ancestral G+C contents obtained from a nonhomogeneous model, or on the resulting inferences about the evolution of thermophyly. This theoretical effort should be useful for the study of protein adaptation, which presumably proceeds in a typical covarion-like manner.