  We present a complete and optimal set of observables for the exclusive 4-body
B meson decay B -> K*(->K pi) l+l- in the low dilepton mass region, that
contains a maximal number of clean observables. This basis of observables is
built in a systematic way. We show that all the previously defined observables
and any observable that one can construct, can be expressed as a function of
this basis. This set of observables contains all the information that can be
extracted from the angular distribution in the cleanest possible way. We
provide explicit expressions for the full and the uniangular distributions in
terms of this basis. The conclusions presented here can be easily extended to
the large-q^2 region. We study the sensitivity of the observables to
right-handed currents and scalars. Finally, we present for the first time all
the symmetries of the full distribution including massive terms and scalar
contributions.
