  We give a general criterion for conformal embeddings of vertex operator
algebras associated to affine Lie algebras at arbitrary levels. Using that
criterion, we construct new conformal embeddings at admissible rational and
negative integer levels. In particular, we construct all remaining conformal
embeddings associated to automorphisms of Dynkin diagrams of simple Lie
algebras. The semisimplicity of the corresponding decompositions is obtained by
using the concept of fusion rules for vertex operator algebras.
