  Let $G$ be a finite group and $\phi : V\to W$ an equivariant morphism of
finite dimensional $G$-modules. We say that $\phi$ is faithful if $G$ acts
faithfully on $\phi(V)$. The covariant dimension of $G$ is the minimum of the
dimension of $\bar{\phi(V)}$ taken over all faithful $\phi$. In \cite{KS07} we
investigated covariant dimension and were able to determine it in many cases.
Our techniques largely depended upon finding homogeneous faithful covariants.
After publication of \cite{KS07}, the junior author of this article pointed out
several gaps in our proofs. Fortunately, this inspired us to find better
techniques, involving multihomogeneous covariants, which have enabled us to
extend and complete the results, simplify the proofs and fill the gaps of
\cite{KS07}.
