  We introduce a CR-invariant class of Lorentzian metrics on a circle bundle
over a 3-dimensional CR-structure, which we call quasi-Fefferman metrics. These
metrics generalise the Fefferman metric but allow for more control of the Ricci
curvature. Our main result is a criterion for embaddability of 3-dimensional
CR-structures in terms of the Ricci curvature of the quasi-Fefferman metrics in
the spirit of the results by Hill et al.
