  We present a determination of the decay constants of the $D$ and $D_s$ mesons
from lattice QCD, each with a total error of about 2%, approximately a factor
of three better than previous calculations. We have been able to achieve this
through the use of a highly improved discretization of QCD for charm quarks,
coupled to gauge configurations generated by the MILC collaboration that
include the full effect of sea u, d, and s quarks. We have results for a range
of u/d masses down to m_s/5 and three values of the lattice spacing, which
allow us to perform accurate continuum and chiral extrapolations. We fix the
charm quark mass to give the experimental value of the \eta_c mass, and then a
stringent test of our approach is the fact that we obtain correct (and
accurate) values for the mass of the D and D_s mesons. We compare f_D and
f_{D_s} with f_K and f_\pi, and using experiment determine corresponding CKM
elements with good precision.
