  Using data collected with the CLEO detector operating at the CESR e+e-
collider at sqrt s = 3.97-4.26 GeV, we investigate 15 charmonium decay modes of
the psi(4040), psi(4160), and Y(4260) resonances. We confirm, at 11$\sigma$
significance, the BaBar Y(4260) --> pi+ pi- J/psi discovery, make the first
observation of Y(4260) --> pi0 pi0 J/psi (5.1 sigma), and find the first
evidence for Y(4260) --> K+ K- J/psi (3.7 sigma). We measure e+e-
cross-sections at sqrt s = 4.26 GeV as sigma(pi+ pi- J/psi) = 58 +12-10 +- 4
pb, sigma(pi0 pi0 J/psi) = 23 +12 -8 +- 1 pb, and sigma(K+ K- J/psi) = 9 +9 -5
+- 1 pb, in which the uncertainties are statistical and systematic,
respectively. Upper limits are placed on other decay rates from all three
resonances.
