The transition towards a low-carbon infrastructure requires an understanding of the embodied carbon (eCO₂) associated with concrete. However, much current work on eCO₂ underestimates the complexity of its relationship with concrete mix design. This paper demonstrates how eCO₂ of concrete is not a simple function of strength. Rather, for a given strength, considerable eCO₂ savings can be made by careful attention to basic mix design. Replacement of cement with PFA (pulverised fuel ash) can achieve considerable savings; additionally, using a concrete of lower workability, employing a superplasticiser, using crushed rather than rounded aggregate and using a higher strength of cement can have comparably significant effects. The analysis is presented in terms of embodied carbon per unit strength; this shows that there is an optimum strength for all concretes (with regard to minimising eCO₂ per unit of structural performance) of between 50 and 70MPa.