Using e(+)e(-) collision data corresponding to 5.88 x 10(6)Y(3S) [25.9 x 10(6)psi (2S)] decays and acquired by the CLEO III [ CLEO- c] detectors operating at the Cornell Electron Storage Ring, we study the singlepion 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 BY(3S) -> pi(0)h(b)) < 1.2 X 10(-3) at 90% confidence level, and measure B(psi(2S) -> (pi(0)h(c)) = (9.0 +/- 1.5 +/- 1.3) x 10(-4). Signal sensitivities are enhanced by excluding very asymmetric pi(0) -> gamma gamma candidates.