We compute the decay constants of the pseudoscalar mesons D and D_s using a linear combination of finite energy sum rules which minimize the contribution of the unknown continuum spectral function. We employ the recent three loop calculation of the pseudoscalar two-point function expanded in powers of the running charm quark mass. The theoretical uncertainties arising from the QCD asymptotic expansion are quite relevant in this case due to the relative small scale of the charm mass. We obtain the following results: f_D = 177±21 MeV and f_{D_s} = 205±22 MeV. These results, within the error bars, are in good agreement with estimates obtained using Borel transform QCD sum rules, but somewhat smaller than results of recent lattice computations.