  We revisit QCD sum rules for the decay constants of heavy-light mesons. In
the sum rules for the vector mesons B^*_(s) and D^*_(s) we improve the accuracy
of OPE, taking into account the O(alpha_s^2) terms in the perturbative part and
calculating the O(alpha_s) corrections to the quark-condensate contribution.
With this accuracy, we obtain the ratios of decay constants: f_B^*/f_B=1.02
+0.07 -0.03, f_D^*/f_D=1.20 +0.10 -0.07. The sum rule predictions for the decay
constants of pseudoscalar mesons are updated with the results f_B=(207 +17 -9)
MeV, f_B_s=(242 +17 -12) MeV, f_D=(201 +12 -13) MeV, f_D_s=(238 +13 -23) MeV.
In order to assess the sensitivity of our calculation to the form of the sum
rule, we consider alternative versions such as the power moments and Borel sum
rules with different weights of the spectral density. We also investigated the
heavy quark limit of the sum rules for vector and pseudoscalar mesons,
estimating the violations of the heavy-quark spin and flavour symmetry.
