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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, westudy the single-pion transitions from Y(3S) [psi(2S)] to the respectivespin-singlet states h_{b[c]}. Utilizing only the momentum of suitably selectedtransition-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 excludingvery asymmetric pi^0 -> gamma gamma candidates.

Branching fractions for Y(3S) -> pi^0 h_b and psi(2S) -> pi^0 h_c