Background. Rodentia is the most diverse order of placental mammals, with extant rodent species representing about half of all placental diversity. In spite of many morphological and molecular studies, the family-level relationships among rodents and the location of the rodent root are still debated. Although various datasets have already been analyzed to solve rodent phylogeny at the family level, these are difficult to combine because they involve different taxa and genes. Results. We present here the largest protein-coding dataset used to study rodent relationships. It comprises six nuclear genes, 41 rodent species, and eight outgroups. Our phylogenetic reconstructions strongly support the division of Rodentia into three clades: (1) a "squirrel-related clade", (2) a "mouse-related clade", and (3) Ctenohystrica. Almost all evolutionary relationships within these clades are also highly supported. The primary remaining uncertainty is the position of the root. The application of various models and techniques aimed to remove non-phylogenetic signal was unable to solve the basal rodent trifurcation. Conclusion. Sequencing and analyzing a large sequence dataset enabled us to resolve most of the evolutionary relationships among Rodentia. Our findings suggest that the uncertainty regarding the position of the rodent root reflects the rapid rodent radiation that occurred in the Paleocene rather than the presence of conflicting phylogenetic and non-phylogenetic signals in the dataset.