  Let $\Omega$ be a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$. Let
$1\leq q_{0}\leq (n-1)$. We show that if $q_{0}$--sums of eigenvalues of the
Levi form are comparable, then if the Diederich--Forn\ae ss index of $\Omega$
is $1$, the $\overline{\partial}$--Neumann operators $N_{q}$ and the Bergman
projections $P_{q-1}$ are regular in Sobolev norms for $q_{0}\leq q\leq n$. In
particular, for domains in $\mathbb{C}^{2}$, Diederich--Forn\ae ss index $1$
implies global regularity in the $\overline{\partial}$--Neumann problem.
