We study the impact of B->Kpill decays on B->K*(->Kpi)ll, taking into account the K* at finite width. Interference effects can generically be sizable, up to O(10%), but are reduced in several ratios of observables of the angular distribution. Information on strong phases is central to control interference effects, which cannot be removed by sideband subtractions. We point out ways to probe the strong phases; only a single one is required to describe leading effects in the region of low hadronic recoil. We find that recent LHCb data on the B0->K*0mumu angular observables at low recoil are in good agreement with the standard model.