We propose a new method for estimating the radiative transitions between the excited 1- charmonium levels and ηc. The method is based on QCD (plus the hypothesis of local duality) and makes no reference to the standard potential picture. It is argued that the decay ψ′(3.698)→ηcγ is essentially due to the gluon admixture in the Ψ′ wave function. The most naive analysis yields approximately 0.15 keV for the ψ′→ηcγ decay width, five times smaller than preliminary data. The experimental number for Γ(ψ′→ηcγ)-0.7 keV-can be reproduced only at a price of introducing a rather large ψ″(3.772)→ηcγ amplitude, Γ(ψ″→ηcγ)∼1 keV. As a byproduct, we get a reliable prediction for the ρ→πγ decay rate, Γ(ρ→πγ)≈70 keV, in good agreement with a recent measurement.