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 Bs → l+ l- where l = e, μ, 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 (Bs → 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 (Bs → l+ l-) and the branching ratios of these decays can be as large as present experimental upper bounds. If future experiments measure B (Bs → 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 (Bs → l+ l- γ) subject to the present experimental constraints on B → (K, K*) l+ l- and B → K* γ. New physics in form scalar/pseudoscalar, which makes a very large contribution to Bs → l+ l-, makes no contribution at all to Bs → l+ l- γ 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* γ. In both cases, enhancement of B (Bs → l+ l- γ) much beyond the SM expectation is impossible. In conclusion, present data on B → (K, K*) transitions allow for large B (Bs → l+ l-) but do not allow B (Bs → l+ l- γ) to be much larger than its SM expectation. © 2007 Elsevier B.V. All rights reserved.