A pulsed jet cavity Fourier transform microwave spectrometer has been used to measure the rotational spectra of OCCuX (X = F, Cl, Br) in the frequency range 5-21 GHz. Metal atoms were generated via laser ablation and were allowed to react with CO and a halide precursor, prior to stabilization of the products within a supersonic jet. These are the first experimental observations of OCCuF and OCCuBr and the first high-resolution spectroscopic study of gas-phase OCCuCl. All three molecules were found to be linear. Rotational constants, centrifugal distortion constants, nuclear quadrupole coupling constants, and nuclear spin-rotation coupling constants have been precisely determined. The rotational constants have been used to evaluate the various bond lengths, and the results are in good agreement with the trend established for OCAuX species. The C-O distance is found to be comparatively short and close to that of free CO. The M-C distance is longer than that predicted by ab initio calculations, and the Cu-X distances are very similar to those observed in the corresponding metal halides. Vibrational wavenumbers have been estimated from the distortion constants and are compared with the results of various ab initio studies. Changes in the Cu, Cl, and Br nuclear quadrupole coupling constants indicate that substantial charge rearrangement takes place on coordination with CO, consistent with the formation of strong Cu-C bonds. Mulliken orbital population analyses have been performed and provide evidence of pi -back-donation from Cu in all of the species studied. The evaluated nuclear spin-rotation coupling constants have been used to estimate the Cu-63 nuclear shielding constants, sigma, and their spans (Omega) in (OCCuF)-Cu-63, (OCCuCl)-Cu-63-Cl-35, and (OCCuBr)-Cu-63-Br-79.