The branching fractions of decays of the Ds+ meson normalize many measurements of processes involving charm quarks. Using 298 /pb of e+ e- collisions recorded by the CLEO-c detector at the Cornell Electron Storage Ring, we determine absolute branching fractions for eight Ds+ decays with a double tag technique. In particular we determine the branching fraction B(Ds+ -> K- K+ pi+) = (5.50 +- 0.23 +- 0.16)%, where the uncertainties are statistical and systematic respectively. The uncertainty in these determinations is roughly a factor of two better than previous world averages. We also search for possible CP asymmetries and provide partial branching fractions for kinematic subsets of the K- K+ pi+ decay mode.