Extracting short distance information from b -> s l+ l- effectively

We point out that in inclusive B -> Xs l+ l- decay an angular decomposition provides a third (q^2 dependent) observable sensitive to a different combination of Wilson coefficients than the rate and the forward-backward asymmetry. Since a precise measurement of q^2 dependence requires large data sets, it is important to consider the data integrated over regions of q^2. We develop a strategy to extract all measurable Wilson coefficients in B -> Xs l+ l- from a few simple integrated rates in the low q^2 region. A similar decomposition in B -> K* l+ l-, together with the B -> K* \gamma rate, also provides a determination of the Wilson coefficients, without reliance on form factor models and without having to measure the zero of the forward-backward asymmetry.