We use QCD sum rules, together with two different numerical algorithms
, for predicting masses of first excited states and, as a byproduct, p
artial decay widths of ground states in various channels of Charmonium
. In particular we apply the method to the S-1(o) channel and to the P
-1(1) channel. Our predictions on first excited states (m(r/c) 3575(-1
8)(+30) MeV, (h/c) = 4355(-26)(+37)MeV) and on partial decay widths (G
amma(eta c+2 gamma) = 5585(-635)(+490) eV, Gamma(hc-->3q) = 515-803 ke
V) are consistent with present (poor) data and agree with most predict
ions done by other methods.