  One of Pierre Molino's principal mathematical achievements was his theory of
Riemannian foliations. One of his last papers, published in 2001, showed that
his theory could be extended to a large class of non-integrable distributions.
The key example here is that of a \emph{respectful decomposition} of a Lie
algebra $\mathfrak{g}$; this is vector space decomposition $\mathfrak{g}=H+V$
such that $[V,H]\subseteq H$. This paper will examine the basic properties of
respectful decompositions.
