The presence of a sizable CP-violating phase in B-s-(B) over bar (s) mixing
would be an unambiguous signal of physics beyond the standard model. We an
alyze various possibilities to detect such a new phase considering both tag
ged and untagged decays. The effects of a sizable width difference Delta Ga
mma between the B-s mass eignstates, on which the untagged analyses rely, a
re included in all formulas. A novel method to find this phase from simple
measurements of lifetimes and branching ratios in untagged decays is propos
ed. This method does not involve two-exponential fits, which require much l
arger statistics. For the tagged decays, an outstanding role is played by t
he observables of the time-dependent angular distribution of the B-s-->J/ps
i[-->l(+)l(-)]phi[-->K+K-] decay products. We list the formulas needed for
the angular analysis in the presence of both a new CP-violating phase and a
sizable Delta Gamma, and propose methods to remove a remaining discrete am
biguity in the new phase. This phase can therefore be determined in an unam
biguous way.