  Extending a result of He to the non-integrable case of K-contact manifolds,
it is shown that transverse Hermitian scalar curvature may be interpreted as a
moment map for the strict contactomorphism group. As a consequence, we may
generalize the Sasaki-Futaki invariant to K-contact geometry and establish a
number of elementary properties. Moreover, we prove that in dimension 5 certain
deformation-theoretic results can be established also under weaker
integrability conditions by exploiting the relationship between
J-anti-invariant and self-dual 2-forms.
