  I consider rare CP-violating decay modes $\eta(\eta')\to\pi\pi$ and note that
an interaction that leads to such decays would necessarily induce a nucleon
electric dipole moment (EDM). The experimental limits for the corresponding
branching ratios are quite soft. I relate these decay branching ratios to the
value of the induced nucleon EDM and translate the experimental limits on the
neutron EDM into much more stringent constraints on these decay rates:
$\frac{\Gamma_{\eta\to\pi\pi}}{\Gamma_\eta}\lesssim3.5\times10^{-14}$ and
$\frac{\Gamma_{\eta'\to\pi\pi}}{\Gamma_\eta'}\lesssim1.8\times10^{-17}$.
