We argue that monetary policies in euro-candidate countries should also aim at mitigating excessive instability of the key target and instrument variables of monetary policy during turbulent market periods. Our empirical tests show a significant degree of leptokurtosis, thus prevalence of tail-risks, in the conditional volatility series of such variables in the euro-candidate countries. Their central banks will be well-advised to use both standard and unorthodox (discretionary) tools of monetary policy to mitigate such extreme risks while steering their economies out of the crisis and through the euroconvergence process. Such policies provide flexibility that is not embedded in the Taylor-type instrument rules, or in the Maastricht convergence criteria.