  We consider real forms of Lie algebras and embeddings of sl(2) which are
consistent with the construction of integrable models via Hamiltonian
reduction. In other words: we examine possible non-standard reality conditions
for non-abelian Toda theories. We point out in particular that the usual
restriction to the maximally non-compact form of the algebra is unnecessary,
and we show how relaxing this condition can lead to new real forms of the
resulting W-algebras. Previous results for abelian Toda theories are recovered
as special cases. The construction can be extended straightforwardly to deal
with osp(1|2) embeddings in Lie superalgebras. Two examples are worked out in
detail, one based on a bosonic Lie algebra, the other based on a Lie
superalgebra leading to an action which realizes the N=4 superconformal
algebra.
