The covarion (COV)-like properties of sequences are poorly described and their impact on phylogenetic analyses poorly understood. We demonstrate using simulations that, under an evolutionary model where the proportion of variable sites changes in nonadjacent lineages, log likelihood values for rates across site (RAS) and COV models become similar, making models difficult to distinguish. Further, although COV and RAS models provide a great improvement in likelihood scores over a homogeneous model with these simulated data, reconstruction accuracy of tree building is low, suggesting caution when it is suspected that proportions of variable sites differ in different evolutionary lineages. We study the performance of a recently developed contingency test that detects the presence of COV-type evolution modified for protein data. We report that if proportions of variable sites (p(var)) change in a lineage-specific manner such that their distributions in different lineages become sufficiently nonoverlapping, then the contingency test can incorrectly suggest a homogeneous model. Also of concern is the possibility of different proportions of variable sites between the groups being studied. In a study of chloroplast proteins, interpretation of the test is found to be susceptible to different partitioning of taxon groups, making the test very subjective in its implementation. Extreme intergroup differences in the extent of divergence and difference in proportions of variable sites could be contributing to this effect.