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\u27\u27 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\u27\u27 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
