  We consider the most general new physics effective Lagrangian for b--> s l+
l-. We derive the upper limit on the branching ratio for the processes B_s-->
l^+ l- where l=e, mu, subject to the current experimental bounds on related
processes, B--> (K,K*) l+ l-. If the new physics interactions are of
vector/axial-vector form, the present measured rates for B--> (K,K*) l+ l-
constrain B_s--> l+ l to be of the same order of magnitude as their respective
Standard Model (SM) predictions. On the other hand, if the new physics
interactions are of scalar/pseudoscalar form, B--> (K,K*) l+ l- rates do not
impose any useful constraint on B_s--> l+ l- and the branching ratios of these
decays can be as large as present experimental upper bounds. If future
experiments measure B_s--> l+ l- to be > 10^{-8} then the new physics giving
rise to these decays has to be of the scalar/pseudoscalar form. We also
consider the effect of new physics on B_s--> l+ l- gamma subject to the present
experimental constraints on B--> (K,K*) l+ l- and B--> K* gamma. New physics in
form scalar/pseudoscalar, which makes a very large contribution to B_s--> l+
l-, makes no contribution at all to B_s--> l+ l- gamma due to angular momentum
conservation. New Physics in the form of vector/axial-vector operators is
constrained by the data on B--> (K,K*) l+ l- and new physics in the form of
tensor/pseudo-tensor is constrained by the data on B--> K* gamma. In both
cases, enhancement of B_s--> l+ l- gamma much beyond the SM expectation is
impossible. In conclusion, present data on B-->(K,K*) transitions allow for
large B(B_s--> l+ l-) but do not allow B(B_s--> l+ l- gamma) to be much larger
than its SM expectation.
