For the past four decades the compositional organization of the mammalian genome posed a formidable challenge to molecular evolutionists attempting to explain it from an evolutionary perspective. Unfortunately, most of the explanations adhered to the "isochore theory," which has long been rebutted. Recently, an alternative compositional domain model was proposed depicting the human and cow genomes as composed mostly of short compositionally homogeneous and nonhomogeneous domains and a few long ones. We test the validity of this model through a rigorous sequence-based analysis of eleven completely sequenced mammalian and avian genomes. Seven attributes of compositional domains are used in the analyses: (1) the number of compositional domains, (2) compositional domain-length distribution, (3) density of compositional domains, (4) genome coverage by the different domain types, (5) degree of fit to a power-law distribution, (6) compositional domain GC content, and (7) the joint distribution of GC content and length of the different domain types. We discuss the evolution of these attributes in light of two competing phylogenetic hypotheses that differ from each other in the validity of clade Euarchontoglires. If valid, the murid genome compositional organization would be a derived state and exhibit a high similarity to that of other mammals. If invalid, the murid genome compositional organization would be closer to an ancestral state. We demonstrate that the compositional organization of the murid genome differs from those of primates and laurasiatherians, a phenomenon previously termed the "murid shift," and in many ways resembles the genome of opossum. We find no support to the "isochore theory." Instead, our findings depict the mammalian genome as a tapestry of mostly short homogeneous and nonhomogeneous domains and few long ones thus providing strong evidence in favor of the compositional domain model and seem to invalidate clade Euarchontoglires.