  A frequent topic in the study of pattern avoidance is identifying when two
sets of patterns $\Pi, \Pi'$ are Wilf equivalent, that is, when
$|\text{Av}_n(\Pi)| = |\text{Av}_n(\Pi')|$ for all $n$. In recent work of Dokos
et al. the notion of Wilf equivalence was refined to reflect when avoidance of
classical patterns preserves certain statistics. In this article, we continue
their work by examining $\text{des}$-Wilf equivalence when avoiding certain
non-classical patterns.
