Pleurocarpous mosses, characterized by lateral female gametangia and highly branched, interwoven stems, comprise three orders and some 5000 species, or almost half of all moss diversity. Recent phylogenetic analyses resolve the Ptychomniales as sister to the Hypnales plus Hookeriales. Species richness is highly asymmetric with approximately 100 Ptychomniales, 750 Hookeriales, and 4400 Hypnales. Chloroplast DNA (cpDNA) sequences were obtained to compare partitioning of molecular diversity among the orders with estimates of species richness, and to test the hypothesis that either the Hookeriales or Hypnales underwent a period (or periods) of exceptionally rapid diversification. Levels of biodiversity were quantified using explicitly historical "phylogenetic diversity" and non-historical estimates of standing sequence diversity. Diversification rates were visualized using lineage-through-time (LTT) plots, and statistical tests of alternative diversification models were performed using the methods of Paradis ...