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Increasing genetic wheat yield potential is considered by many as critical to increasing global wheat yields and production, baring major changes in consumption patterns. Climate change challenges breeding by making target environments less predictable, altering regional productivity and potentially increasing yield variability. Here we used a crop simulation model solution in the SIMPLACE framework to explore yield sensitivity to select trait characteristics (radiation use efficiency [RUE], fruiting efficiency and light extinction coefficient) across 34 locations representing the world’s wheat-producing environments, determining their relationship to increasing yields, yield variability and cultivar performance. The magnitude of the yield increase was trait-dependent and differed between irrigated and rainfed environments. RUE had the most prominent marginal effect on yield, which increased by about 45 % and 33 % in irrigated and rainfed sites, respectively, between the minimum and maximum value of the trait. Altered values of light extinction coefficient had the least effect on yield levels. Higher yields from improved traits were generally associated with increased inter-annual yield variability (measured by standard deviation), but the relative yield variability (as coefficient of variation) remained largely unchanged between base and improved genotypes. This was true under both current and future climate scenarios. In this context, our study suggests higher wheat yields from these traits would not increase climate risk for farmers and the adoption of cultivars with these traits would not be associated with increased yield variability.