The tetragonal-to-orthorhombic phase transition at Ts, which precedes the antiferromagnetic phase transition at TN in many iron-based superconductors, is considered one of the manifestations of electronic nematic order. By constructing temperature-pressure phase diagrams of pure and Co-doped BaFe2As2, we study the relation of Ts and TN under pressure p. Our data disclose two qualitatively different regimes in which ΔT=Ts−TN either increases or decreases with p. We provide experimental evidence that the transition between the two regimes may be associated with sudden changes of the Fermi surface topology. Therefore, our results not only support the electronic origin of the structural order, but also emphasize the importance of details of the Fermi surface for the evolution of nematic order under pressure.