The increasing spread of conservation agriculture demands that the next generation of wheat varieties includes cultivars capable of maintaining satisfactory yields with lower inputs and under uncertain climate scenarios. On the basis of the genetic gains achieved during decades of selection oriented to yield improvements under conventional crop management, it is important that novel breeding targets are defined and addressed. Grain yield, yield-related traits, and phenological and morphological characteristics, as well as functional quality parameters have been analyzed for six varieties each of bread and durum wheat, under minimum tillage and no-tillage. During the three-year experiment, the climatic conditions at the field trial site were characterized by low rainfall, although different degrees of aridity—from moderate to severe—were experienced. Differences were found between these two soil management practices in regard to the varieties’ yield stability. A positive influence of no-tillage on traits related to grain and biomass yield was also evidenced, and some traits among the examined seemed involved in varietal adaptation to a particular non-conventional tillage system. The study also confirmed some breeding targets for improved performance of wheat genotypes in conservation agroecosystems. These traits were represented in the small set of traditional varieties analysed.