  We prove that every connected graph $G$ with $m$ edges contains a set $X$ of
at most $\frac{3}{16}(m + 1)$ vertices such that $G-X$ has no $K_4$ minor, or
equivalently, has treewidth at most $2$. This bound is best possible.
Connectivity is essential: If $G$ is not connected then only a bound of
$\frac{1}{5}m$ can be guaranteed.
