We discuss the three independent asymmetries, AT(2)(q2), AT(im)(q2) and AT(re)(q2), that one can build from the amplitudes A⊥(q2) and A∥(q2). These quantities are expected to be accessible from the new B-physics experiments, they are sensitive to the presence of new physics, and they are not very sensitive to hadronic uncertainties. Studying their low q2 dependence can be helpful in discerning among various possible new physics scenarios. All three asymmetries can be extracted from the full angular analysis of B→K⁎ℓ+ℓ−. Our formulas apply to both the massless and the massive lepton case.