  Using e^+e^- collision data corresponding to 5.88M Y(3S) [25.9M psi(2S)]
decays and acquired by the CLEO III [CLEO-c] detectors operating at CESR, we
study the single-pion transitions from Y(3S) [psi(2S)] to the respective
spin-singlet states h_{b[c]}. Utilizing only the momentum of suitably selected
transition-pi^0 candidates, we obtain the upper limit B(Y(3S) -> pi^0 h_b) <
1.2\times 10^{-3} at 90% confidence level, and measure B(psi(2S) -> pi^0 h_c) =
(9.0+-1.5+-1.3)\times 10^{-4}. Signal sensitivities are enhanced by excluding
very asymmetric pi^0 -> gamma gamma candidates.
