Water deficiency is a major constraint to wheat productivity in drought prone regions. The wheat DELLA‐encoding height‐reducing genes (Rht) are associated with significant increase in grain yield. However, the knowledge of their benefit in dry environments is insufficient. The objective of the study was to examine the effect of induced drought on leaf water content, level of oxidative stress, cell membrane stability, accumulation of osmoprotectants and activity of some antioxidant enzymes in wheat near‐isogenic lines carrying the alleles Rht‐B1b (semidwarfing) and Rht‐B1c (dwarfing) in comparison with the tall control Rht‐B1a. Six‐day‐long water deprivation was imposed at seedling stage. Plants carrying Rht‐B1c and, to a lesser extent, those carrying Rht‐B1b performed better under stress compared with Rht‐B1a in terms of more sustained membrane integrity, enhanced osmoregulation and better antioxidant defence. These differential responses could reflect pleiotropic effects of the Rht‐B1 gene associated with the accumulation of the mutant gene product, that is, altered DELLA proteins, or might be related to allelic variations at neighbouring loci carrying candidate genes for proteins with a major role in plant water regulations and stress adaptation. These findings might be of importance to breeders when introducing Rht‐B1 alleles into wheat cultivars designed to be grown in drought liable regions.