  We describe along the guidelines of Kohn "Quantitative estimates..." (1999),
the constant E_s which is needed to control the commutator of a totally real
vector field T with di-bar* in order to have Sobolev s-regularity of the
Bergman projection in any degree of forms, on a smooth pseudoconvex domain D of
the complex space. This statement, not explicit in Kohn's paper, yields
Straube's Theorem in "A sufficient condition..." (2008). Next, we refine the
pseudodifferential calculus at the boundary in order to relate, for a defining
function r of D, the operators (T^+)^{-delta/2} and (-r)^{delta/2}. We are thus
able to extend to general degree of forms the conclusion of Kohn which only
holds for functions: if for the Diederich-Fornaess index delta of D, we have
that (1-\delta)^{1/2} < E_s, then the Bergman projection is s-regular.
