  We present in detail the calculation of the virtual O(alpha_s) corrections to
the inclusive semi-leptonic rare decay b --> s l+ l-. We also include those
O(alpha_s) bremsstrahlung contributions which cancel the infrared and mass
singularities showing up in the virtual corrections. In order to avoid large
resonant contributions, we restrict the invariant mass squared s of the lepton
pair to the range 0.05 < s/mb^2 < 0.25. The analytic results are represented as
expansions in the small parameters s/mb^2, z = mc^2/mb^2 and s/(4 mc^2). The
new contributions drastically reduce the renormalization scale dependence of
the decay spectrum. For the corresponding branching ratio (restricted to the
above s-range) the renormalization scale uncertainty gets reduced from +/-13%
to +/-6.5%.
