Wheat is a major source of energy and nutrition worldwide, but it is also a primary cause of frequent diet-induced health issues, specifically celiac disease, for which the only effective therapy so far is strict dietary abstinence from gluten-containing grains. Wheat gluten proteins are grouped into two major categories: high-molecular-weight glutenin subunits (HMWgs), vital for mixing and baking properties, and gliadins plus low-molecular-weight glutenin subunits (LMWgs) that contain the overwhelming majority of celiac-causing epitopes. We put forth a hypothesis that eliminating gliadins and LMWgs while retaining HMWgs might allow the development of reduced-immunogenicity wheat genotypes relevant to most gluten-sensitive individuals. This hypothesis stems from the knowledge that the molecular structures and regulatory mechanisms of the genes encoding the two groups of gluten proteins are quite different, and blocking one group's transcription, without affecting the other's, is possible. The genes for gliadins and LMWgs have to be de-methylated by 5-methylcytosine DNA glycosylase/lyase (DEMETER) and an iron-sulfur (Fe-S) cluster biogenesis enzyme (DRE2) early during endosperm development to permit their transcription. In this study, a TILLING (Targeting Induced Local Lesions IN Genomes) approach was undertaken to identify mutations in the homoeologous DEMETER (DME) and DRE2 genes in common and durum wheat. Lines with mutations in these genes were obtained that displayed reduced content of immunogenic gluten proteins while retaining essential baking properties. Although our data at first glance suggest new possibilities for treating celiac disease and are therefore of medical and agronomical interest, it also shows that inducing mutations in the DME and DRE2 genes analyzed here affected pollen viability and germination. Hence there is a need to develop other approaches in the future to overcome this undesired effect.