  Brans-Dicke gravity admits spherical solutions describing naked singularities
rather than black holes. Depending on some parameters entering such a solution,
stable circular orbits exist for all radius. One argues that, despite the fact
that the naked singularity is an infinite redshift location, the far observed
orbital motion frequency is unbounded for an adiabatically decreasing radius.
This is a salient difference with General Relativity, and the incidence on the
gravitational radiation by EMRI systems is stressed. Since this behaviour
survives the infinite omega limit, the possibility of such solutions is of
utmost interest in the new gravitational wave astronomy context, despite the
current constraints on scalar-tensor gravity.
