The decays D-s(+/-) -> mu(+/-)nu(mu) and D-s(+/-) -> tau(+/-)nu(tau) have traditionally been used to measure the D-s(+/-) meson decay constant f(Ds). Recent measurements at CLEO-c and the B factories suggest a branching ratio for both decays somewhat higher than the Standard Model prediction using f(Ds) from unquenched lattice calculations. The charged Higgs boson (H-+/-) in the Two Higgs Doublet Model (Type II) would also mediate these decays, but any sizeable contribution from H-+/- can only suppress the branching ratios and consequently is now slightly disfavoured. It is shown that constraints on the parameters tan beta and m(H +/-) from such decays can be competitive with and complementary to analogous constraints derived from the leptonic meson decays B-+/- -> tau(+/-)nu(tau) and K-+/- -> mu(+/-)nu(mu), especially if lattice calculations eventually prefer f(Ds) < 250 MeV.
