  The Levi geometry at weakly pseudoconvex boundary points of domains in C^n, n
\geq 3, is sufficiently complicated that there are no universal model domains
with which to compare a general domain. Good models may be constructed by
bumping outward a pseudoconvex, finite-type \Omega \subset C^3 in such a way
that: i) pseudoconvexity is preserved, ii) the (locally) larger domain has a
simpler defining function, and iii) the lowest possible orders of contact of
the bumped domain with \bdy\Omega, at the site of the bumping, are realised.
When \Omega \subset C^n, n\geq 3, it is, in general, hard to meet the last two
requirements. Such well-controlled bumping is possible when \Omega is
h-extendible/semiregular. We examine a family of domains in C^3 that is
strictly larger than the family of h-extendible/semiregular domains and
construct explicit models for these domains by bumping.
