We update the branching ratios for the inclusive decays B#->#X_sl"+l"- and the exclusive decays B#->#(K,K"*)l"+l"-, with l=e, #mu#, in the standard model by including the explicit O(#alpha#_s) and #LAMBDA#_Q_C_D/m_b corrections. This framework is used in conjunction with the current measurements of the branching ratios for B#->#X_s#gamma# and B#-># Kl"+l"- decays and upper limits on the branching ratios for the decays B#->#(K"*,X_s)l"+l"- to work out bounds on the Wilson coefficients C_7, C_8, C_9 and C_1_0 appearing in the effective Hamiltonian formalism. The resulting bounds are found to be consistent with the predictions of the standard model and some variants of supersymme...