Lattice NRQCD with leading finite lattice spacing errors removed is used to
simulate heavy-heavy vector decay constants. Quenched simulations are perf
ormed at three values of the coupling and fifteen values of the quark mass.
The improved gauge action with plaquettes and rectangles is used. Landau l
ink improvement is used throughout. "Perturbative" and nonperturbative meso
n masses are compared. One-loop perturbative matching between lattice and c
ontinuum heavy-heavy vector currents is performed. The data is consistent w
ith a f(V) proportional to root M-V a.