The relationships of passerines (such as the well-studied zebra finch) with non-passerine birds is one of the great enigmas of avian phylogenetic research, because decades of extensive morphological and molecular studies yielded highly inconsistent results between and within data sets. Here we show the first application of the virtually homoplasy-free retroposon insertions to this controversy. Our study examined ∼200,000 retroposon-containing loci from various avian genomes and retrieved 51 markers resolving early bird phylogeny. Among these, we obtained statistically significant evidence that parrots are the closest and falcons the second-closest relatives of passerines, together constituting the Psittacopasserae and the Eufalconimorphae, respectively. Our new and robust phylogenetic framework has substantial implications for the interpretation of various conclusions drawn from passerines as model organisms. This includes insights of relevance to human neuroscience, as vocal learning (that is, birdsong) probably evolved in the psittacopasseran ancestor, >30 million years earlier than previously assumed.