In wheat, night-time transpiration rate (TRN) could amount to 14-55% of daytime transpiration rate (TR), depending on the cultivar and environment. Recent evidence suggests that TRN is much less responsive to soil drying than daytime TR, and that such 'wasteful' water losses would increase the impact of drought on yields. In contrast, other evidence indicates that pre-dawn, circadian increases in TRN may enable enhanced radiation use efficiency, resulting in increased productivity under water deficit. Until now, there have been no attempts to evaluate these seemingly conflicting hypotheses in terms of their impact on yields in any crop. Here, using the Mediterranean environment of Tunisia as a case study, we undertook a simulation modelling approach using SSM-Wheat to evaluate yield outcomes resulting from these TRN trait modifications. TRN represented 15% of daytime TR-generated yield penalties of up to 20%, and these worsened when TRN was not sensitive to soil drying TR. For the same TRN level (15%), simulating a predawn increase in TRN alleviated yield penalties, leading to yield gains of up to 25%. Overall, this work suggests that decreasing TRN but increasing pre-dawn circadian control would be a viable breeding target to increase drought tolerance in a Mediterranean environment.