On any smooth compact connected manifold M of dimension m >= 2 admitting a smooth non- trivial circle action S =\{S-t\}(t is an element of S)1 and for every Liouville number alpha is an element of S-1 we prove the existence of a C-infinity-diffeomorphism f is an element of A(alpha) = <(\{h circle S-alpha circle h(-1) : h is an element of Diff(infinity) (M, nu)\})over bar>(C infinity) with a good approximation of type (h, h+1), a maximal spectral type disjoint with its convolutions and a homogeneous spectrum of multiplicity two for the Cartesian square f x f. This answers a question of Fayad and Katok ({[}10, Problem 7.11]). The proof is based on a quantitative version of the approximation by conjugation-method with explicitly defined conjugation maps and tower elements.