For the first time broadening by both resonance and dispersive-inductive in
teractions with H-atoms are included in the formation of Balmer lines in co
ol stars, without the use of a multipole expansion. Comparison of synthetic
profiles with observed profiles for the Sun and two late F dwarfs shows th
at this improvement in broadening theory accounts for some of the problems
found in previous work. It is anticipated that planned future developments
in the theory of self broadening will lead to further improvements in the m
odelling of cool star atmospheres.