There is widespread evidence of lineage-specific rate variation, known as 
heterotachy, during protein evolution. Changes in the structural and functional 
constraints acting on a protein can lead to heterotachy, and it is plausible 
that such changes, known as covarion shifts, may affect many amino acids at 
once. Several previous attempts to model heterotachy have used covarion models, 
where the sequence undergoes covarion drift, whereby each site may switch 
independently among a set of discrete classes having different substitution 
rates. However, such independent switching may not capture biologically 
important events where the selective forces acting on a protein affect many 
sites at once. We describe a new class of models that allow the rates of 
substitution and switching to vary among branches of a phylogenetic tree. Such 
models are better able to handle covarion shifts. We apply these models to a set 
of genes occurring in nonphotosynthetic bacteria, cyanobacteria, and the 
plastids of green and red algae. We find that 4/5 genes show evidence of some 
form of rate switching and that 3/5 genes show evidence that the relative 
switching rate differs among taxonomic groups. We conclude that covarion shifts 
may be frequent during the deep evolution of plastid genes and that our 
methodology may provide a powerful new tool for investigating such shifts in 
other systems.