  We analyze the angular distributions of B -> K^* (-> K pi) l^+ l^- and B -> K
l^+ l^- decays in the region of low hadronic recoil in a model-independent way
by taking into account the complete set of dimension-six operators [sbar Gamma
b][lbar Gamma' l]. We obtain several novel low-recoil observables with high
sensitivity to non-standard-model Dirac structures, including CP-asymmetries
which do not require flavor tagging. The transversity observables H_T^(1,3,4,5)
are found to be insensitive to hadronic matrix elements and their uncertainties
even when considering the complete set of operators. In the most general
scenario we show that the low recoil operator product expansion can be probed
at the few-percent level using the angular observable J_7. Higher sensitivities
are possible assuming no tensor contributions, specifically by testing the
low-recoil relation |H_T^(1)|=1. We explicitly demonstrate the gain in reach of
the low-recoil observables in accessing the ratio |C_9/C_10| compared to the
forward-backward asymmetry, and probing CP-violating right-handed currents Im
C_10'. We give updated Standard Model predictions for key observables in B ->
K^(*) l^+ l^- decays.
