  Exploiting recently proposed novel improvements of the techniques used for
extracting from QCD sum rules pivotal hadron characteristics, including their
systematic errors, we succeed to achieve a conspicuous agreement of the
predictions of QCD sum rules for the decay constants $f_B$ and $f_{B_s}$ of the
heavy pseudoscalar mesons $B$ and $B_s,$ which before tended to be slightly too
large, with corresponding results from lattice QCD. Adopting for the crucial
$b$-quark $\bar{\rm MS}$ mass the value $\bar{m}_b(\bar{m}_b)=(4.247\pm0.034)$
GeV, we get $f_B=(192.0\pm14.6)$ MeV and $f_{B_s}=(228.0\pm19.8)$ MeV; clearly,
this may be also viewed as a determination of the $b$-quark mass from
sufficiently precise decay constants.
