  For direct CP-violation in $K\to\pi\pi$ decays, the usual isospin-breaking
effects at the percent level are amplified by the dynamics behind the $\Delta
I=1/2$ rule and conventionally encoded in $\Omega_{\rm IB}$ parameters. The
updated prediction $\Omega_{\rm IB}^{(8)}=(15.9\pm 8.2)\times 10^{-2}$ of the
Chiral Perturbation Theory for the strong isospin-breaking due to
$\pi_3-\eta_8$ mixing confirms such a tendency but is quite sensitive to the
theoretical input value of the low-energy constant corresponding to the
flavour-singlet $\eta_0$ exchange contribution in this truncated octet scheme.
We rather exploit the phenomenological $\eta_8-\eta_0$ mixing as a probe for
the non-negligible flavour-singlet component of the physical $\eta$ pole to
find $\Omega_{\rm IB}^{(9)}=(35\pm7)\times 10^{-2}$ in a complete nonet scheme.
A large central value in the nonet scheme is thus substituted for a large
uncertainty in the octet one. Including the experimental $\pi^+-\pi^0$ mass
difference as the dominant electromagnetic isospin-breaking, we obtain for the
effective parameter entering the ratio $\epsilon'/\epsilon$ an improved result
$\hat\Omega_{\rm eff}^{(9)}=(29\pm7)\times 10^{-2}$ to be compared with
$\hat\Omega_{\rm eff}^{(8)}=(17\pm9)\times 10^{-2}$ used in recent analyses of
$\epsilon'/\epsilon$. Accordingly, we get a reduction from
$(\epsilon'/\epsilon)_{\rm SM}^{(8)}=(17.4\pm 6.1)\times 10^{-4}$ to
$(\epsilon'/\epsilon)_{\rm SM}^{(9)}=(13.9\pm 5.2)\times 10^{-4}$ and thereby
an effective suppression of $(\epsilon'/\epsilon)_{\rm SM}$ by isospin-breaking
corrections as large as $40\%$ relative to the recent RBC-UKQCD value.
