  We investigate rare semileptonic \bar B -> \bar K^* l^+ l^- decays, providing
a comprehensive treatment of theoretical uncertainties in the low-q^2 region as
needed for interpreting current and future LHCb and B-factory data in terms of
the new physics search. We go beyond the usual focus on form-factor
uncertainties, paying proper attention to non-factorizable terms.
  A central point is the systematic exploitation of the V-A structure of SM
weak interactions, which leads to the suppression of two helicity amplitudes
and some of the angular coefficients. We review how this works at the level of
(helicity) form factors, and show that the hierarchies extend to
non-factorizable terms. For virtual charm effects, we give an argument for it
in terms of light-cone QCD sum rules that continues to hold at the level of
"long-distance" Lambda_QCD^2/m_c^2 power corrections, reducing an important
source of theoretical uncertainty in any \bar B, \bar B_s -> V l^+ l^- (or \bar
B -> V gamma) decay. The contributions of the remaining hadronic weak
Hamiltonian respect a similar hierarchy. We employ a resonance model to
preclude (in the \bar B -> \bar K^* case) large long-distance corrections to
this.
  A phenomenological part pays particular attention to the region of lowest
dilepton mass, 4 m_l^2 <= q^2 <= 2 GeV^2. Two observables remain theoretically
clean, implying a (theoretical) sensitivity to the real (imaginary) part of the
"right-handed" Wilson coefficient C_7' to 10% (1%) of C_7^SM, both in the
muonic and the electronic mode. We also show that there are two near-exact
relations between angular coefficients, even in the presence of new physics and
when lepton masses are not neglected.
