It is argued that the J gY→η(η′)γ decay rates are directly calculable within quantum chromodynamics. The calculation of Γ( J Ψ→ηγ) is most straightforward and involves no new hypotheses as compared to, say, the J Ψ→e+e- decay in detail earlier. To the contrary, evaluation of the J Ψ→η′γ width puts on trial dynamical results concerning the η′ coupling to gluons. The latter depends crucially on non-perturbative power terms in the QCD sum rules. The calculated numbers for Γ( J Ψ→ηγ) and Γ( J Ψ→η′γ) agree well with the data.