  From electron-positron collision data collected with the CLEO detector
operating at CESR near \sqrt{s}=10.6 GeV, improved measurements of the
branching fractions for tau decays into three explicitly identified hadrons and
a neutrino are presented as {\cal
B}(\tau^-\to\pi^-\pi^+\pi^-\nu_\tau)=(9.13\pm0.05\pm0.46)%, {\cal B}(\tau^-\to
K^-\pi^+\pi^-\nu_\tau)=(3.84\pm0.14\pm0.38)\times10^{-3}, {\cal B}(\tau^-\to
K^-K^+\pi^-\nu_\tau)=(1.55\pm0.06\pm0.09)\times10^{-3}, and {\cal B}(\tau^-\to
K^-K^+K^-\nu_\tau)<3.7\times10^{-5} at 90% C.L., where the uncertainties are
statistical and systematic, respectively.
