  Neutron diffraction measurements are presented measuring the responses of
both magnetic and structural order parameters of parent and lightly Co-doped
Ba(Fe{1-x}Co{x})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 T_N as Co-doping is increased and the
superconducting phase is approached. Additionally, as uniaxial pressure is
increased within parent and lightly-doped Ba(Fe{1-x}Co{x})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.
