  The presence of a sizeable CP-violating phase in B_s^0-B_s^0-bar mixing would
be an unambiguous signal of physics beyond the Standard Model. We analyse
various possibilities to detect such a new phase considering both tagged and
untagged decays. The effects of a sizeable width difference Delta Gamma between
the B_s mass eigenstates, on which the untagged analyses rely, are included in
all formulae. A novel method to find this phase from simple measurements of
lifetimes and branching ratios in untagged decays is proposed. This method does
not involve two-exponential fits, which require much larger statistics. For the
tagged decays, an outstanding role is played by the observables of the
time-dependent angular distribution of the B_s -> J/psi [-> l^+ l^-] \phi [->
K^+K^-] decay products. We list the formulae needed for the angular analysis in
the presence of both a new CP-violating phase and a sizeable Delta Gamma, and
propose methods to remove a remaining discrete ambiguity in the new phase. This
phase can therefore be determined in an unambiguous way.
