  The conformal bootstrap is applied to percolation and dilute self-avoiding
polymers, two theories with Virasoro central charge $c=0$ in two dimensions. In
both cases we propose a spectrum of operators motivated by Virasoro symmetry
which is devoid of a stress energy tensor as an approximate means of enforcing
$c=0$. Percolation is treated in $2\leq D \leq 6$ dimensions, and the
self-avoiding walk in $2 \leq D \leq 4$.
