  The number of Frattini chief factors or of chief factors which are
complemented by a maximal subalgebra of a finite-dimensional Lie algebra $L$ is
the same in every chief series for $L$, by \cite[Theorem 2.3]{[11]}. However,
this is not the case for the number of chief factors which are simply
complemented in $L$. In this paper we determine the possible variation in that
number.
