Chromosome 1R of rye is a useful source of genes for disease resistance and enhanced agronomic performance in wheat. One of the most prevalent genes transferred to wheat from rye is the stem rust resistance gene Sr31. The recent emergence and spread of a stem rust pathotype virulent to this gene has refocused efforts to find and utilize alternative sources of resistance. There has been considerable effort to transfer a stem rust resistance gene, SrR, from Imperial rye, believed to be allelic to Sr31, into commercial wheat cultivars. However, the simultaneous transfer of genes at the Sec-1 locus encoding secalin seed storage proteins and their association with quality defects preclude the deployment of SrR in some commercial wheat breeding programs. Previous attempts to induce homoeologous recombination between wheat and rye chromosomes to break the linkage between SrR and Sec-1 whilst retaining the tightly linked major loci for wheat seed storage proteins, Gli-D1 and Glu-D3, and recover good dough quality characteristics, have been unsuccessful. We produced novel tertiary wheat–rye recombinant lines carrying different lengths of rye chromosome arm 1RS by inducing homoeologous recombination between the wheat 1D chromosome and a previously described secondary wheat–rye recombinant, DRA-1. Tertiary recombinant T6-1 (SrR+ Sec-1–) carries the target gene for stem rust resistance from rye and retains Gli-D1 but lacks the secalin locus. The tertiary recombinant T49-7 (SrR– Sec-1+) contains the secalin locus but lacks the stem rust resistance gene. T6-1 is expected to contribute to wheat breeding programs in Australia, whereas T49-7 provides opportunities to investigate whether the presence of secalins is responsible for the previously documented dough quality defects.