Band-tail states are routinely invoked in models of a-Si:H, including defect pool models and models of light-induced defects. These models describe the band-tail states as being localized on a single stretched bond. However, to our knowledge, there is no theoretical or experimental work to justify these assumptions. In this work we use ab initio calculations to support earlier tight-binding calculations that show that the band-tail states are very delocalized—involving large numbers of atoms as the energy is varied from midgap into the tails. Our work also shows that valence-band-tail states are statistically associated with short bonds ~not long bonds!, and conduction-band states with long bonds. We have slightly modified a 512-atom model of a-Si due to Djordjevic, Thorpe, and Wooten @Phys. Rev. B 52, 5688 ~1995!# to produce a large model of a-Si:H with realistic band tails, radial distribution function, and vibrational spectrum. Above all, we created and used a model with no spectral or geometrical defects. @S0163-1829~98!03148-8#