Synchrotron X-ray powder diffraction was used to study the high pressure dependence of the lattice parameter and structural evolution of the monoclinic La2LiRuO6 and tetragonal Sr2CoMoO6, Sr2CuWO6, and Ba2CuWO6 double perovskite phases. The c lattice parameters of Sr2CuWO6 and Ba2CuWO6 decreased more rapidly than the a lattice parameters and Ba2CuWO6 exhibited a more anisotropic compression compared to Sr2CuWO6. Based on lower pressure refinements of Ba2CuWO6, the anisotropic compression is proposed to be due to the preferential compression of the Cu–O bonds containing cooperative Jahn–Teller distortions aligned parallel to the c-axis, which is in contrast to Sr2CoMoO6, where the change in the octahedral tilting and symmetric bond compression is the prevailing compression mechanism. The bulk moduli were obtained from a fit of the volume–pressure data using the second-order Murnaghan equation of state.