A broad-line region (BLR) disc model is derived and fitted to 121 published broad emission-line profiles from quasistellar objects (QSOs) and Seyfert I galaxies. Keplerian rotation of material in calm circular orbits, plus stimulated non-isotropic emission is best suited to explain the observed profiles. BLR discs in QSOs are, within the framework of the model, found to be tapered and extensive, whereas Seyfert I discs are usually fanned out but equally extensive. The material density in each disc appears to be constant with radius. In QSO emission-line profiles, the peak relative to adjacent continuum intensity increases with increasing logarithm of disc mass or maximum radius, on average.