  By establishing a unified estimate of the twisted Kohn-Morrey-H\"{o}rmander
estimate and the $q$-pseudoconvex Ahn-Zampieri estimate, we discuss variants of
Property $(P_q)$ of Catlin and Property $(\widetilde{P_q})$ of McNeal on the
boundary of a smooth pseudoconvex domain in $\mathbb{C}^n$ for certain high
level forms. These variant conditions on the one side, imply $L^2$-compactness
of the $\overline{\partial}$-Neumann operator on the associated domain, on the
other side, are different from the classical Property $(P_q)$ and Property
$(\widetilde{P_q})$. As an application of our result, we show that if the
Hausdorff $(2n-2)$-dimensional measure of the weakly pseudoconvex points on the
boundary of a smooth bounded pseudoconvex domain is zero, then the
$\overline{\partial}$-Neumann operator $N_{n-1}$ is $L^2$-compact on
$(0,n-1)$-level forms. This result generalizes Boas and Sibony's results on
$(0,1)$-level forms.
