  We present a sum-rule calculation of the decay constants of the charmed
vector mesons $D^*$ and $D^*_s$ from the two-point correlator of vector
currents. First, we show that the perturbative expansion in terms of the pole
mass exhibits no sign of convergence whereas the reorganization of this
expansion in terms of the $\overline{\rm MS}$ mass leads to a distinct
hierarchy. Second, making use of the operator product expansion in terms of the
$\overline{\rm MS}$ mass, we determine the decay constants of the $D^*$ and
$D^*_s$ mesons with an emphasis on the uncertainties in these theoretically
predicted quantities related both to the input QCD parameters and to the
limited accuracy of the method of sum rules. Our results are $f_{D^*}=(252.2
\pm 22.3_{\rm OPE}\pm 4_{\rm syst})\; {\rm MeV}$ and $f_{D_s^*}=(305.5 \pm
26.8_{\rm OPE}\pm 5_{\rm syst})\; {\rm MeV}$. For the ratios of the
vector-to-pseudoscalar decay constants we report $f_{D^*}/f_D= 1.221\pm
0.080_{\rm OPE}\pm 0.008_{\rm syst}$ and $f_{D^*_s}/f_{D_s}= 1.241\pm
0.057_{\rm OPE}\pm 0.007_{\rm syst}$.
