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The rare multi-body decays B->K pi ll and B_s->K K ll are both important asbackgrounds to precision analyses in the benchmark modes B->K* ll and B_s->phill as well as sensitive probes of flavor physics in and beyond the standardmodel. We work out non-resonant contributions to B->K pi ll and B_s->K K llamplitudes, where l=e,mu, at low hadronic recoil in a model-independent way.Using the operator product expansion in 1/m_b, we present expressions for thefull angular distribution. The latter allows to probe new combinations of|Delta B|=|Delta S|=1 couplings and gives access to strong phases betweennon-resonant and resonant contributions. Exact endpoint relations betweentransversity amplitudes based on Lorentz invariance are obtained. Severalphenomenological distributions including those from the angular projections tothe S-, P-, D-waves are given. Standard model branching ratios for non-resonantB->K pi ll and B_s->K K ll decays are found to be in the few 10^{-8} region,but drop significantly if cuts around the K* or phi mass are employed.Nevertheless, the non-resonant contributions to B->K pi ll provide the dominantbackground in the B->K* ll signal region with respect to the low mass scalars.In B_s->K K ll, the narrowness of the phi allows for more efficient backgroundcontrol. We briefly discuss lepton-flavor non-universal effects, also in viewof the recent data on R_K.

The $\bar B \to \bar K \pi \ell \ell$ and $\bar B_s \to \bar K K \ell \ell$ distributions at low hadronic recoil