The mass of the strange quark is determined from SU(3)-breaking effects in the tau hadronic width. Compared to previous analyses, the contributions from scalar and pseudoscalar spectral functions, which suffer from large perturbative corrections, are replaced by phenomenological parametrisations. This leads to a sizeable reduction of the uncertainties in the strange mass from tau decays. Nevertheless, the resulting m(s) value is still rather sensitive to the moment of the invariant mass distribution which is used for the determination, as well as the size of the quark-mixing matrix element \V-us\. Imposing the unitarity fit for the CKM matrix, we obtain m(s)(2 GeV) = 117 +/- 17 MeV, whereas for the present Particle Data Group average for \V-us\, we find m(s)(2 GeV) = 103 +/- 17 MeV. On the other hand, using an average of m(s) from other sources as an input, we are able to calculate the quark-mixing matrix element \V-us\, and we demonstrate that if the present measurement of the hadronic decay of the tau into strange particles is improved by a factor of two, the determination of \V-us\ is more precise than the current world average.