  We report determination of branching fractions for the decays psi(2S) --> h +
J/psi, where h=any, pi+pi-, pi0pi0, eta, pi0, and gamma gamma through
chi_{c0,1,2}. These measurements use 27M psi(2S) decays produced in e+e-
collision data collected with the CLEO detector. The resulting branching
fractions and ratios thereof improve upon previously achieved precision in all
cases, and in combination with other measurements permit determination of
B(chi_cJ --> gamma J/psi) and B(psi(2S) --> light hadrons).
