  We study the Sasaki cone of a CR structure of Sasaki type on a given closed
manifold. We introduce an energy functional over the cone, and use its critical
points to single out the strongly extremal Reeb vectors fields. Should one such
vector field be a member of the extremal set, the scalar curvature of a Sasaki
extremal metric representing it would have the smallest $L^2$-norm among all
Sasakian metrics of fixed volume that can represent vector fields in the cone.
We use links of isolated hypersurface singularities to produce examples of
manifolds of Sasaki type, many of these in dimension five, whose Sasaki cone
coincides with the extremal set, and examples where the extremal set is empty.
We end up by proving that a conjecture of Orlik concerning the torsion of the
homology groups of these links holds in the five dimensional case.
