The phylogenetic diversification of Hexapoda is still not fully understood. Morphological and molecular analyses have resulted in partly contradicting hypotheses. In molecular analyses, 18S sequences are the most frequently employed, but it appears that 18S sequences do not contain enough phylogenetic signals to resolve basal relationships of hexapod lineages. Until recently, character interdependence in these data has never been treated seriously, though possibly accounting for the occurrence of biased results. However, software packages are readily available which can incorporate information on character interdependence within a Bayesian approach. Accounting for character covariation derived from a hexapod consensus secondary structure model and applying mixed DNA/RNA substitution models, our Bayesian analysis of 321 hexapod sequences yielded a partly robust tree that depicts many hexapod relationships congruent with morphological considerations. It appears that the application of mixed DNA/RNA models removes many of the anomalies seen in previous studies. We focus on basal hexapod relationships for which unambiguous results are missing. In particular, the strong support for a "Chiastomyaria" clade (Ephemeroptera+Neoptera) obtained in Kjer's [2004. Aligned 18S and insect phylogeny. Syst. Biol. 53, 1-9] study of 18S sequences could not be confirmed by our analysis. The hexapod tree can be rooted with monophyletic Entognatha but not with a clade Ellipura (Collembola+Protura). Compared to previously published contributions, accounting for character interdependence in analyses of rRNA data presents an improvement of phylogenetic resolution. We suggest that an integration of explicit clade-specific rRNA structural refinements is not only possible but an important step in the optimization of substitution models dealing with rRNA data.