  Completely regular tensionful codimension-n brane world solutions are
discussed, where the core of the brane is chosen to be a thin codimension-(n-1)
shell in an infinite volume flat bulk, and an Einstein-Hilbert term localized
on the brane is included (Dvali-Gabadadze-Porrati models). In order to support
such localized sources we enrich the vacuum structure of the brane by the
inclusion of localized form fields. We find that phenomenological constraints
on the size of the internal core seem to impose an upper bound to the brane
tension. Finite transverse-volume smooth solutions are also discussed.
