  Let $M$ be a closed manifold of Sasaki type. A polarization of $M$ is defined
by a Reeb vector field, and for one such, we consider the set of all Sasakian
metrics compatible with it. On this space, we study the functional given by the
squared $L^2$-norm of the scalar curvature. We prove that its critical points,
or canonical representatives of the polarization, are Sasakian metrics that are
transversally extremal. We define a Sasaki-Futaki invariant of the
polarization, and show that it obstructs the existence of constant scalar
curvature representatives. For a fixed CR structure of Sasaki type, we define
the Sasaki cone of structures compatible with this underlying CR structure, and
prove that the set of polarizations in it that admit a canonical representative
is open.
