We have made a precise measurement of the absolute branching fractions of B-s(0) -> D-s(()()+) D-s(()()-) decays using 121.4 fb(-1) of data recorded by the Belle experiment running at the Upsilon(5S) resonance. The results are B(B-s(0) -> D-s(+) D-s(-)) = 0.58(-0.09)(+0.11) +/- 0.13)%, B(B-s(0) -> D-s*(+/-) D-s(-/+)) = (1.76(-0.22)(+0.23) +/- 0.40)%, and B(B-s(0) -> D-s*(+) D-s*(-)) = (1.98(-0.31-0.50)(+0.33+0.52))%; the sum is B(B-s(0) -> D-s(()()+) D-s(()()-)) = (4.32(-0.39-1.03)(+0.42+1.04))%. Assuming B-s(0) -> D-s(()()+) D-s(()()-) saturates decays to CP-even final states, the branching fraction constrains the ratio Delta Gamma(s)/cos phi(12), where Delta Gamma(s) is the difference in widths between the two B-s-(B) over bar (s) mass eigenstates, and phi(12) is the CP-violating phase in B-s-(B) over bar (s) mixing. We also measure for the first time the longitudinal polarization fraction of B-s(0) -> D-s*(+) D-s*(-); the result is 0.06(-0.17)(+0.18) +/- 0.03. DOI: 10.1103/PhysRevD.87.031101