  We observe signals for the decays psi(3770)--> X J/psi from data acquired
with the CLEO detector operating at the CESR e^+e^- collider with sqrt{s}=3773
MeV. We measure the following branching fractions B(psi(3770)--> XJ/psi) and
significances: (189 +- 20 +- 20) x 10^-5 (11.6sigma) for X=pi^+pi^-, (80 +- 25
+- 16) x 10^-5 (3.4sigma) for X=pi^0pi^0, and (87 +- 33 +- 22) x 10^-5
(3.5sigma) for X=eta, where the errors are statistical and systematic,
respectively. The radiative return process e^+e^- -->gamma psi(2S) populates
the same event sample and is used to measure Gamma_{ee}[psi(2S)]=(2.54 +- 0.03
+- 0.11) keV.
