All recent studies of bird phylogeny have produced poorly resolved relationships among the orders of Neoaves, the lineage that includes most modern birds. This “bush” result suggests the possibility of an explosive and potentially unresolvable evolutionary radiation. However, simultaneous radiations of multiple lineages are thought to be rare or nonexistent in nature and difficult to corroborate empirically because lack of phylogenetic resolution can also be caused by analytical artifacts. Here we examine the predictions of the explosive radiation hypothesis for five independent genetic datasets for Neoaves. We propose a methodology for testing for polytomies of evolutionary lineages, perform likelihood-ratio tests to compare trees with zero-length branches to more resolved trees, compare topologies between independent gene trees, and propose a power test for the SOWH test. The evidence of (1) extremely short (in some cases zero-length) branches for interordinal relationships across independent gene trees and (2) topological incongruence among gene trees suggests that the bird tree includes essentially simultaneous radiation of multiple lineages. This result explains why a robust phylogeny of birds has not been produced despite much effort on the part of avian systematists.