We present the results of x-ray diffraction and x-ray absorption spectroscopy experiments in CuAlO(2) under high pressure. We discuss the polarization dependence of the x-ray absorption near-edge structure at the Cu K-edge. XRD under high pressure evidences anisotropic compression, the a-axis being more compressible than the c-axis. EXAFS yields the copper-oxygen bond length, from which the only internal parameter of the delafossite structure is deduced. The combination of anisotropic compression and the internal parameter decrease results in a regularization of the AlO(6) octahedra. The anisotropic compression is related to the chemical trends observed in the lattice parameters when Al is substituted by other trivalent cations. Both experiments evidence the existence of an irreversible phase transition that clearly manifests at 35 ± 2 GPa. The structure of the high-pressure polymorph could not be determined, but it implies a change of the Cu environment, which remains anisotropic. Precursor effects are observed from the lowest pressures, which are possibly related to crystal breaking at a submicroscopic scale with partial reorientation of the crystallites.