An extension of the Monte Carlo Singular System Analysis (MC SSA) is described, based on evaluating and testing regularity of dynamics of the SSA modes against the colored noise null hypothesis, in addition to the test based on variance (eigenvalues). The application of the regularity index, computed from a coarse-grained estimation of mutual information, enhances the test sensitivity and reliability in detection of relatively more regular dynamical modes than those obtained by decomposition of colored noises, in particular, in detection of irregular oscillations embedded in red noise. This enhanced MC SSA is successfully applied in detection of period 7.8 years oscillatory modes in records of monthly average near-surface air temperature from several European locations, as well as in the monthly North Atlantic Oscillation index.