  There are known to be integrable Sutherland models associated to every real
root system -- or, which is almost equivalent, to every real reflection group.
Real reflection groups are special cases of complex reflection groups. In this
paper we associate certain integrable Sutherland models to the classical family
of complex reflection groups. Internal degrees of freedom are introduced,
defining dynamical spin chains, and the freezing limit taken to obtain static
chains of Haldane-Shastry type. By considering the relation of these models to
the usual BC_N case, we are led to systems with both real and complex
reflection groups as symmetries. We demonstrate their integrability by means of
new Dunkl operators, associated to wreath products of dihedral groups.
