  A nonrelativistic Hamiltonian with plausible spin dependent corrections is
proposed for the quarkonia below their respective strong decay thresholds. With
only six free parameters this model reproduces the nine known masses of the
bottomonia within about 1 MeV, the six known masses of the charmonia within a
few MeV and the five known leptonic decay widths of the ${}^3S_1$ states within
about {20 %}. The model is then used to predict the masses of the remaining 43
quarkonia (some of them for the first time) and of the leptonic decay widths of
the two ${}^1S_0(\bar{b}c)$ states. Comparison with some other models is made.
