Both cylindrical (''magic ring'') and spherical (''magic sphere'') dip
olar Permanent magnet field sources are capable of providing arbitrari
ly high fields in their interior cavities. However, since the obtainab
le field increases only logarithmically with the structural radius, fi
elds above about 2.5 T necessitate excessively massive and costly stru
ctures if working volumes of more than a few cm3 are desired. The pres
ent work shows how for some cavity shapes the structures can be modifi
ed to produce fields up to 4.0 T with only about one fifth the mass an
d bulk of the conventional structures. Possible applications which wou
ld be impractical with the unmodified field sources are cited.