We present detailed scattering models confirming that distinctive variations in polarization across the broad Hα line, which are observed in a significant fraction of type 1 Seyfert galaxies, can be understood in terms of a rotating line-emitting disc surrounded by a coplanar scattering region (the equatorial scattering region). The predicted polarization properties are: (i) averaged over wavelength, the position angle (PA) of polarization is aligned with the projected disc rotation axis and hence also with the radio source axis; (ii) the polarization PA rotates across the line profile, reaching equal but opposite (relative to the continuum PA) rotations in the blue and red wings; and (iii) the degree of polarization peaks in the line wings and passes through a minimum in the line core. We identify 11 objects that exhibit these features to different degrees. In order to reproduce the large-amplitude PA rotations observed in some cases, the scattering region must closely surround the emission disc and the latter must itself be a relatively narrow annulus – presumably the Hα-emitting zone of a larger accretion disc. Asymmetries in the polarization spectra may be attributable to several possible causes, including bulk radial infall in the equatorial scattering region, or contamination by polar scattered light. The broad Hα lines do not, in general, exhibit double-peaked profiles, suggesting that a second Hα-emitting component of the broad-line region is present, in addition to the disc.