  We deal with compact Kaehler manifolds M which are acted on by a semisimple
compact Lie group G of isometries with codimension one regular orbits. We
provide an explicit description of the standard blow-ups of such manifolds
along complex singular orbits, in case b_1(M) = 0 and the regular orbits are
Levi nondegenerate. Up to very few exceptions, all the nonhomogeneous manifolds
in this class are shown to admit a G-invariant Kaehler-Einstein metric, giving
completely new examples of compact Kaehler-Einstein manifolds.
