  We present NNLL results for the double differential decay width dGamma(b ->
X_s l+ l-)/(dsh dcos(theta)), where theta is the angle between the momenta of
the b-quark and the l+, measured in the rest-frame of the lepton pair. From
these results we also derive NNLL results for the lepton forward-backward
asymmetries. Genuinely new calculations for the combined virtual- and gluon
bremsstrahlung corrections associated with the operators O_7, O_9 and O_10 are
necessary. We find that the NNLL corrections drastically reduce the
renormalization scale dependence of the forward-backward asymmetries. In
particular, sh_0, the position at which the forward-backward asymmetries
vanish, is essentially free of uncertainties due to the renormalization scale
at NNLL precision. We find sh_0(NNLL)=0.162 +/- 0.005, where the error is
dominated by the uncertainty in (m_c/m_b). This is to be compared with
sh_0(NLL)=0.144 +/- 0.020, where the error is dominated by uncertainties due to
the choice of mu.
