Measurements of the branching fractions of purely leptonic decays of B-mesons translate into constraints in the plane of the charged Higgs mass versus tan {beta} which are relatively insensitive to the particular theoretical model. Using the full BABAR dataset of 450 million B-decays we search for these decays. No significant signal is found in the decays into electrons or muons and we set upper limits on the branching fractions of the order of a 10{sup -6} at 90% confidence level. We measure the branching fraction of B {yields} {tau}{mu} to be (1.7 {+-} 0.6) x 10{sup -4}.