In order to investigate the near wing of the Lyman- α line, accurate line profile calculations and molecular data are both required due to the existence of a close line satellite responsible for its asymmetrical shape. Lyman- α lines observed with the Cosmic Origin Spectograph on the Hubble Space Telescope show this peculiarity in the spectra of DBA and DA white dwarf stars. A similar asymmetrical shape in the blue wing can be predicted in the Balmer- α line of H perturbed by He and H atoms. In continuation with a very recent work on the Lyman- α line, where the n = 2 potential energies and transition dipole moments from the ground state were determined, we present new accurate H-He potential energies and electronic transition dipole moments involving the molecular states correlated with H( n = 3)+He and their transition dipole moments with the states correlated with H( n = 2)+He. Those new data and existing molecular data for H( n = 2,3)-H are used to provide a theoretical investigation of the collisional effects in the blue wing of the Balmer- α line of H perturbed by He and H atoms. We note the consequences for the Balmer- α line shape in the physical conditions found in the cool atmosphere of DZA white dwarfs where helium densities may be as high as 10 21 cm −3 . This study is undertaken with a unified theory of spectral line broadening valid at very high helium densities.