The dimensional stability in stressed states of concrete made with ternary Portland cements containing limestone is not well understood, particularly when the concrete undergoes carbonation. In this study, the dimensional changes of blended slag cements, with and without limestone, under simultaneous compressive stress and accelerated carbonation exposure are reported. Four concretes made with CEM I, CEM I + slag or ternary slag-limestone cements were cured for 7 days before subjecting them to a similar to 30% stress/strength ratio and uniaxial compressive loading under ambient, and accelerated (3% CO2) carbonation exposure up to 28 days. The results show that the creep strain evolution of ternary CEM I-slag concretes with 10 or 20 wt.% limestone addition was comparable to that of binary CEM I-slag concretes, both of which showed lower creep deformation compared to CEM I, under natural or accelerated carbonation exposure. However, greater creep strains were recorded under accelerated carbonation exposure, and the increase was more pronounced in the ternary binder concretes. Under natural exposure conditions, the loaded concretes exhibited less (micro) cracking, which might be potentially reducing the carbonation rates compared to unloaded concretes. The results indicate that partial substitution of CEM I by slag with up to 20% limestone did not significantly reduce carbonation resistance nor dimensional stability of the concrete.