  In the present paper we argue that a special case of the Bach-Weyl metric
describing a static configuration of two Schwarzschild black holes gives rise,
after extending its parameter space to complex values, to a very simple
2-parameter model for the gravitational field of a static deformed mass. We
compare this model, which has no restrictions on the quadrupole parameter, with
the well-known Zipoy-Voorhees $\delta$-metric and show in particular that the
mass quadrupole moment in the latter solution cannot take arbitrary negative
values. We subsequently add an arbitrary angular momentum to our static model
and study some properties of the resulting 3-parameter stationary solitonic
spacetime, which permits us to introduce the notion of the
Fodor-Hoenselaers-Perj\'es relativistic multipole moments.
