  We obtain the static spherically symmetric solutions of a class of
gravitational models whose additions to the General Relativity (GR) action
forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are
selected to maintain the (first) derivative order of the Einstein equations in
Schwarzschild gauge. Generically, the solutions exhibit both horizons and a
singularity at the origin, except for one model that forbids spherical symmetry
altogether. Extensions to arbitrary dimension with a cosmological constant,
Maxwell source and Gauss-Bonnet terms are also considered.
