Phylogenetic analyses of gene and protein sequences have led to two major competing views of the universal phylogeny, the evolutionary tree relating the three kinds of living organisms, Bacteria, Archaea, and Eukarya. In the first scheme, called "the archaebacterial tree, " organisms of the same type are clustered together. In the second scenario, called "the eocyte tree," the archaeal phylum of Crenarchaeota is more closely related to eukaryotes than are other Archaea. A major property of the evolution of functional ribosomal and protein-encoding genes is that the rate of nucleotide and amino acid substitution varies across sequence sites. Here, using distance-based and maximum-likelihood methods, we show that universal phylogenies of ribosomal RNAs and RNA polymerases built by ignoring this variation are biased toward the archaebacterial tree because of attraction between long branches. In contrast, taking among-site rate variability into account gives support for the eocyte tree.