  We construct solutions, for small values of $G$ and angular frequency
$\Omega$, of special relativistic scalar gravity coupled to ideally elastic
matter which have helical but no stationary or axial symmetry. They correspond
to a body without any symmetries in steady rotation around one of its axes of
inertia, or two bodies moving on a circle around their center of gravity. Our
construction is rigorous, but modulo an unproved conjecture on the
differentiability of a certain functional.
