Complexes containing four Cu impurities in Si are systematically investigated using density functional theory. The complexes include various combinations of substitutional and interstitial copper. The structures, formation and binding energies, approximate gap levels, and vibrational spectra are calculated and the results compared to the measured properties of the Cu PL defect. The best candidate out of those investigated is the Cu s1 Cu i3 complex recently proposed by Shirai et al. [J. Phys: Condens. Matter 21, 064249 (2009)]. The estimated positions of the gap levels of Cu s1 Cu in , with n = 0, . . . ,3, suggest a straightforward explanation as to why only the defects Cu s and Cu s1 Cu i3 occur in high-resistivity material.