  We present a new determination of the strong coupling constant from lattice
QCD simulations. We use four different short-distance quantities to obtain the
coupling, three different (infrared) meson splittings to tune the simulation
parameters, and a wide range of lattice spacings, quark masses, and lattice
volumes to test for systematic errors. Our final result consists of ten
different determinations of $\alpha^{(3)}_{P}(8.2 GeV)$, which agree well with
each other and with our previous results. The most accurate of these, when
evolved perturbatively to the $Z^0$ mass, gives $\alpha^{(5)}_{\msbar}(M_Z) =
.1174(24)$. We compare our results with those obtained from other recent
lattice simulations.
