The strange quark mass is extracted from a finite energy sum rule (FESR) an
alysis of the flavor-breaking difference of light-light and light-strange q
uark vector-plus-axial-vector correlators, using spectral functions determi
ned from hadronic tau decay data. We point out problems for existing FESR t
reatments associated with potentially slow convergence of the perturbative
series for the mass-dependent terms in the OPE over certain parts of the FE
SR contour, and show how to construct alternate weight choices which not on
ly cure this problem, but also (1) considerably improve the convergence of
the integrated perturbative series, (2) strongly suppress contributions fro
m the region of s values where the errors on the strange current spectral f
unction are still large and (3) essentially completely remove uncertainties
associated with the subtraction of longitudinal contributions to the exper
imental decay distributions. The result is an extraction of m(s) with stati
stical errors comparable to those associated with the current experimental
uncertainties in the determination of the CKM angle, V-us. We find m(s)(1 G
eV) = 158.6+/-18.7+/-16.3+/-13.3 MeV (where the first error is statistical,
the second due to that on V-us, and the third theoretical).