  If $X$ is a compact set, a {\it topological contraction} is a self-embedding
$f$ such that the intersection of the successive images $f^k(X)$, $k>0$,
consists of one point. In dimension 3, we prove that there are smooth
topological contractions of the handlebodies of genus $\geq 2$ whose image is
essential. Our proof is based on an easy criterion for a simple curve to be
essential in a handlebody.
