Neutron diffraction measurements are presented measuring the responses of both magnetic and structural order parameters of parent and lightly Co-doped Ba(Fe1 xCox)2As2 under the application of uniaxial pressure. We find that the uniaxial pressure induces a thermal shift in the onset of antiferromagnetic order that grows as a percentage of TN as Co doping is increased and the superconducting phase is approached. Additionally, as uniaxial pressure is increased within parent and lightly doped Ba(Fe1 xCox)2As2 on the first-order side of the tricritical point, we observe a decoupling between the onsets of the orthorhombic structural distortion and antiferromagnetism. Our findings place needed constraints on models exploring the nematic susceptibility of the bilayer pnictides in the tetragonal, paramagnetic regime. © 2014 American Physical Society.