Summary: A frequent topic in the study of pattern avoidance is identifying when two sets of patterns \(\Pi, \Pi^\prime\) are Wilf equivalent, that is, when \(|\operatorname{Av}_n(\Pi)| = |\operatorname{Av}_n(\Pi^\prime)|\) for all \(n\). In [T. Dokos et al., Discrete Math. 312, No. 18, 2760–2775 (2012; Zbl 1248.05004)] the notion of Wilf equivalence was refined to reflect when avoidance of classical patterns preserves certain statistics. We continue their work by examining des-Wilf equivalence when avoiding certain nonclassical patterns.