A complex network of trade-offs exists between wheat quality and nutritional traits. We investigated the correlated relationships among several milling and baking traits as well as mineral density in refined white and whole grain flour. Our aim was to determine their pleiotropic genetic control in a multi-parent population over two trial years with direct application to practical breeding. Co-location of major quantitative trait loci (QTL) and principal component based multi-trait QTL mapping increased the power to detect QTL and revealed pleiotropic effects explaining many complementary and antagonistic trait relationships. High molecular weight glutenin subunit genes explained much of the heritable variation in important dough rheology traits, although additional QTL were detected. Several QTL, including one linked to the TaGW2 gene, controlled grain size and increased flour extraction rate. The semi-dwarf Rht-D1b allele had a positive effect on Hagberg falling number, but reduced grain size, specific weight, grain protein content and flour water absorption. Mineral nutrient concentrations were lower in Rht-D1b lines for many elements, in wholemeal and white flour, but potassium concentration was higher in Rht-D1b lines. The presence of awns increased calcium content without decreasing extraction rate, despite the negative correlation between these traits. QTL were also found that affect the relative concentrations of key mineral nutrients compared to phosphorus which may help increase bioavailability without associated anti-nutritional effects of phytic acid. Taken together these results demonstrate the potential for marker-based selection to optimise trait trade-offs and enhance wheat nutritional value by considering pleiotropic genetic effects across multiple traits.