  We study invariant contact p-spheres on principal circle-bundles and solve
the corresponding existence problem in dimension 3. Moreover, we show that
contact p-spheres can only exist on (4n-1)-dimensional manifolds and we
construct examples of contact p-spheres on such manifolds. We also consider
relations between tautness and roundness, a regularity property concerning the
Reeb vector fields of the contact forms in a contact p-sphere.
