  We present an analysis of the m_s^2-corrections to Cabibbo-suppressed tau
lepton decays employing contour improved resummation within an effective scheme
which is an essential new feature as compared to previous analyses. The whole
perturbative QCD dynamics of the tau-system is described by the beta-function
of the effective coupling constant and by two gamma-functions for the effective
mass parameters of the strange quark in different spin channels. We analyze the
stability of our results with regard to high-order terms in the perturbative
expansion of the renormalization group functions. A numerical value for the
strange quark mass in the MS scheme is extracted m_s(M_\tau)=130\pm 27_{exp}\pm
9_{th} MeV. After running to the scale 1 GeV this translates into m_s(1
GeV)=176 \pm 37_{exp}\pm 13_{th} MeV.
