  Recent work suggests the existence of a non-conventional lowest-lying scalar
nonet containing the a0(980). Then the a0(1450) and also the K0*(1430) are
likely candidates to belong to a conventional p-wave $q \bar q$ nonet. However
a comparison of their properties with those expected on this basis reveals a
number of puzzling features. It is pointed out that these puzzles can be
resolved in a natural and robust way by assuming a ``bare'' conventional p-wave
scalar $q \bar q$ nonet to mix with a lighter four quark $qq \bar q \bar q$
scalar nonet to form new ``physical'' states. The essential mechanism is driven
by the fact that the isospinor is lighter than the isovector in the unmixed $qq
\bar q \bar q$ multiplet.
