Key messageSimultaneous genomic selection for grain yield, protein content and dough rheological traits enables the development of resource-use efficient varieties that combine superior yield potential with comparably high end-use quality.AbstractSelecting simultaneously for grain yield and baking quality is a major challenge in wheat breeding, and several concepts like grain protein deviations have been developed for shifting the undesirable negative correlation between both traits. The protein quality is, however, not considered in these concepts, although it is an important aspect and might facilitate the selection of genotypes that use available resources more efficiently with respect to the quantity and quality of the final end products. A population of 480 lines from an applied wheat breeding programme that was phenotyped for grain yield, protein content, protein yield and dough rheological traits was thus used to assess the potential of using integrated genomic selection indices to ease selection decisions with regard to the plethora of quality traits. Additionally, the feasibility of achieving a simultaneous genetic improvement in grain yield, protein content and protein quality was investigated to develop more resource-use efficient varieties. Dough rheological traits related to either gluten strength or viscosity were combined in two separate indices, both of which showed a substantially smaller negative trade-off with grain yield than the protein content. Genomic selection indices based on regression deviations for the two latter traits were subsequently extended by the gluten strength or viscosity indices. They revealed a large merit for identifying resource-use efficient genotypes that combine both superior yield potential with comparably high end-use quality. Hence, genomic selection opens up the opportunity for multi-trait selection in early generations, which will most likely increase the efficiency when developing new and improved varieties.Electronic supplementary materialThe online version of this article (10.1007/s00122-019-03386-1) contains supplementary material, which is available to authorized users.