  We consider graphs $G$ with $\Delta=3$ such that $\chi'(G)=4$ and
$\chi'(G-e)=3$ for every edge $e$, so-called \emph{critical} graphs. Jakobsen
noted that the Petersen graph with a vertex deleted, $P^*$, is such a graph and
has average degree only $\frac83$. He showed that every critical graph has
average degree at least $\frac83$, and asked if $P^*$ is the only graph where
equality holds. A result of Cariolaro and Cariolaro shows that this is true. We
strengthen this average degree bound further. Our main result is that if $G$ is
a subcubic critical graph other than $P^*$, then $G$ has average degree at
least $\frac{46}{17}\approx2.706$. This bound is best possible, as shown by the
Hajos join of two copies of $P^*$.
