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By using a variant Property $(P_q)$ of Catlin, we discuss the relation ofsmall set of weakly pseudoconvex points on the boundary of pseudoconvex domainand compactness of the $\overline{\partial}$-Neumann operator. In particular,we show that if the Hausdorff $(2n-2)$-dimensional measure of the weaklypseudoconvex points on the boundary of a smooth bounded pseudoconvex domain iszero, then the $\overline{\partial}$-Neumann operator $N_{n-1}$ is compact on$(0,n-1)$-level $L^2$-integrable forms.

Hausdorff-$(2n-2)$ dimensional measure zero set and compactness of the $\overline{\partial}$-Neumann operator on $(0,n-1)$ forms