Gravitating discs around a Schwarzschild black hole II

A sequence of exact spacetimes is obtained describing the fields of a Schwarzschild black hole surrounded by stable static axisymmetric thin discs having their inner rim at the least possible radius. In the previous paper we only required stability with respect to perturbations in the disc plane, while it turns out that for discs with relative mass >0.23 the perturbations in perpendicular direction are more dangerous. The discs of the resulting sequence have their inner rims just on, or very close to, circular geodesics marginally stable with respect to either of the perturbations. Redshift from static and Keplerian observers in the disc is computed. The inverted first Morgan-Morgan counter-rotating disc, used in superpositions, has a number of satisfactory physical properties, but it has turned out to have a curvature singularity at the inner rim. However, this is only a consequence of a too steep radial start of density, not present in (inverted) "higher" Morgan-Morgan solutions.