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