  We study effective divisors on $\overline{M}_{0,n}$, focusing on hypertree
divisors introduced by Castravet and Tevelev and the proper transforms of
divisors on $\overline{M}_{1,n-2}$ introduced by Chen and Coskun. Results
include a database of hypertree divisor classes and closed formulas for
Chen--Coskun divisor classes. We relate these two types of divisors, and from
this construct extremal divisors on $\overline{M}_{0,n}$ for $n \geq 7$ that
furnish counterexamples to the conjectural description of the effective cone of
$\overline{M}_{0,n}$ given by Castravet and Tevelev.
