  A subalgebra of a semisimple Lie algebra is wide if every simple module of
the semisimple Lie algebra remains indecomposable when restricted to the
subalgebra. A subalgebra is narrow if the restrictions of all non-trivial
simple modules to the subalgebra have proper decompositions. A semisimple Lie
algebra is regular extreme if any regular subalgebra of the semisimple Lie
algebra is either narrow or wide. Douglas and Repka previously showed that the
simple Lie algebras of type $A_n$ are regular extreme. In this article, we show
that, in fact, all simple Lie algebras are regular extreme. Finally, we show
that no non-simple, semisimple Lie algebra is regular extreme.
