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We reconsider the extraction of the gluon condensates <alpha_s G^2>,<g^3f_{abc} G^3> and the MS running quark masses m_{c,b} from differentM_n(Q^2) Moments and their Ratios by including PT corrections to orderalpha_s^3, NPT terms up to <G^4> and using stability criteria of the resultsversus the degree n (number of Q^2-derivative). We explicitly show that thespectral part of the lowest moment M_1(0) depends strongly (as expected) on itshigh-energy (continuum) contribution, which is minimized for M_{n> 3-4}(0).Using higher moments and the correlations of <alpha_s G^2> with <g^3f_{abc}G^3> and < G^4>, we obtain <alpha_s G^2>=(7.0+- 1.3)10^{-2} GeV^4 and<g^3f_{abc} G^3>=(8.8+- 5.5) GeV^2 <alpha_s G^2>, while our analysis favours amodified factorisation for <G^4>. Using the previous results, we re-determinem_c(m_c) and find that the commonly used M_1(0) lowest moment tends tooverestimate its value compared to the ones from higher moments where stablevalues of m_c(m_c) versus the variations of n and the continuum models arereached. These features can indicate that the quoted errors of m_{c,b} fromM_1(0) may have been underestimated. Optimal results from different high-nmoments converge to the accurate (artithmetic) mean values: m_c(m_c)=1261(16)MeV and m_b(m_b)=4171(14) MeV, in excellent agreement with results obtained in[1] using some judicious choices of ratios of moments.

Gluon Condensates and m_{c,b} from QCD-Moments and their ratios to Order alpha_s^3 and