The sunflower (Helianthus annuus L.) crop in southern Europe suffers from intense and frequent periods of water deficit. Minimisation of water loss in response to water deficit is a major aspect of drought tolerance and can be achieved through the lowering of either leaf area expansion rate or transpiration per unit leaf area (stomatal conductance). During three greenhouse pot experiments, leaf expansion (LE) and transpiration (TR) rates were monitored as the soil dried progressively for about 15 days. This study aimed to quantify the response of these two physiological processes to water deficit, expressed as the fraction of transpirable soil water (FTSW): response thresholds (onset of decline) were estimated on 25 sunflower genotypes from different generations of selection history. From these relationships, the thresholds below which LE and TR started to decrease from the control were calculated: little change was observed until FTSW was close to 0.6 for leaf expansion and 0.4 for daily transpiration. Variability in the response of all genotypes for expansion and transpiration control was better described using specific thresholds for each genotype rather than generic thresholds for sunflower. The ranking of genotypes was found to be unaffected for transpiration rate control, but this was not the case for leaf expansion. Identified response thresholds were not mutually correlated, suggesting that sunflower controls leaf expansion and transpiration rate independently. Neither was correlated with the release date of the genotype, suggesting that these traits were not subject to selection within evaluation environments.