  We review and develop some techniques used to investigate the effective cones
of higher codimension classes. Our results show that a large collection of
boundary strata of rational tails type are extremal in their effective cones on
$\overline{\mathcal{M}}_{g,n}$ and provide evidence for the conjecture that all
boundary strata of $\overline{\mathcal{M}}_{g,n}$ are extremal. As a corollary,
we show that all boundary strata are extremal in genus zero.
