  The leptonic decay $B_s \to \mu^+\mu^-$ is both rare and theoretically clean,
making it an excellent probe for New Physics searches. Due to its helicity
suppression in the Standard Model, this decay is particularly sensitive to new
(pseudo)-scalar contributions. We present a new strategy for detecting
CP-violating New Physics contributions of this kind, exploiting two
observables: $\adg$, which is accessible due to the sizeable decay width
difference of the $B_s$ system, and the mixing-induced CP asymmetry $\smumu$.
We also utilize information from semileptonic $b\to s\mu^+\mu^-$ decays. Using
the currently available experimental information, we find remarkably
constrained regions in the $\adg$--$\smumu$ plane that serve as promising
targets for future measurements.
