The limited fossil evidence for modern (crown) birds during the Cretaceous is consistent with a recent (Palaeogene) radiation; however, molecular clock studies have consistently suggested that modern birds radiated deep in the Mesozoic, with the paucity of fossils prior to the latest Cretaceous explainable by preservational bias. This issue is here addressed using Bayesian methods which integrate stratigraphical and morphological data to simultaneously infer evolutionary relationships and divergence times. These analyses place the diversification of modern birds in the mid-Cretaceous (~100-110Ma), only slightly more recent than many genetic studies, and congruent with latest molecular estimates.