We perform a study of the impact of the recently released limits on BR(Bs ->
mu+ mu-) by LHCb and CMS on several SUSY models. We show that the obtained
constraints can be superior to those which are derived from direct searches for
SUSY particles in some scenarios, and the use of a double ratio of purely
leptonic decays involving Bs -> mu+ mu- can further strengthen such
constraints. We also discuss the experimental sensitivity and prospects for
observation of Bs -> mu+ mu- during the sqrt(s)=7 TeV run of the LHC, and its
potential implications.Comment: 30 pages, 21 figures. v2: Improved discussion of constraints from B
-> tau nu, references adde