  Recently published measurements of the branching ratios ${\cal
B}(\psi(1S)\to\ga \eta_C(1S))$ and ${\cal B}(\psi(2S)\to\ga \eta_C(1S))$ by the
CLEO collaboration are examined in the context of a potential model that
includes both relativistic and one-loop QCD corrections to the quark-antiquark
interaction. The prediction for the width $\Gamma(\psi(1S)\to\ga \eta_C(1S))$
is in excellent agreement with the new data but the prediction for
$\Gamma(\psi(2S)\to\ga \eta_C(1S))$ is too small. In an effort to understand
this discrepancy, we derive an upper bound on $\Gamma(\psi(2S)\to\ga
\eta_C(1S))$ and point out its experimental value saturates this bound.
