  We present the results of the O(alpha_s) two-loop virtual corrections to the
differential decay width dGamma(B -> X_s l+ l-)/ds, where s is the invariant
mass squared of the lepton pair. Those contributions from gluon bremsstrahlung
which are needed to cancel infrared and collinear singularities are also
included. Our calculation is restricted to the range 0.05 < s/mb^2 < 0.25 where
the effects from resonances are small. The new contributions drastically reduce
the renormalization scale dependence of existing results for dGamma(B->X_s l+
l-)/ds. The renormalization scale uncertainty of the corresponding branching
ratio (restricted to range mentioned above) gets reduced from +/-13% to
+/-6.5%.
