Wheat belongs to the most important crops domesticated in the Fertile Crescent. In this region, fortunately, locally adapted wheat landraces are still present in farmers' fields. This material might be of immense value for future breeding programs. However, especially wheat germplasm adapted to the central part of the Fertile Crescent has been poorly characterized for allelic variation at key loci of agricultural importance. Grain hardness is an important trait influencing milling and baking quality of wheat. This trait is mainly determined by three tightly linked genes, namely, Puroindoline a (Pina), Puroindoline b (Pinb), and Grain softness protein-1 (Gsp-1), at the Hardness (Ha-D) locus on chromosome 5DS. To investigate genetic diversity and haplotype structure, we resequenced 96 diverse wheat lines at Pina-D1, Pinb-D1, Gsp-A1, Gsp-B1, and Gsp-D1. Three types of null alleles were identified using diagnostic primers: the first type was a multiple deletion of Pina-D1, Pinb-D1, and Gsp-D1 (Pina-D1k), the second was a Pina-D1 deletion (Pina-D1b); and the third type was a deletion of Gsp-D1, representing a novel null allele designated here as Gsp-D1k. Sequence analysis resulted in four allelic variants at Pinb-D1 and five at Gsp-A1, among them Gsp-A1-V was novel. Pina-D1, Gsp-B1 and Gsp-D1 sequences were monomorphic. Haplotype and phylogenetic analysis suggested that (1) bread wheat inherited its 5DS telomeric region probably from wild diploid Ae. tauschii subsp. tauschii found within an area from Transcaucasia to Caspian Iran; and that (2) the Ha-A and Ha-B homoeoloci were most closely related to sequences of wild tetraploid T. dicocco ides. This study provides a good overview of available genetic diversity at Pina-D1, Pinb-D1, and Gsp-1, which can be exploited to extend the range of grain texture traits in wheat.