The centers formed in silicon as a result of interaction between the substitutional copper impurity (Cus) and interstitial copper (Cui) or hydrogen (H) atoms, which are mobile at room temperature, are investigated in this study using the deep-level transient spectroscopy (DLTS) technique. It is shown that a well-known photoluminescence center, which includes four copper atoms, is formed from Cus via the subsequent addition of Cui. Both intermediate complexes (Cus-Cui and Cus-2Cui) are identified by their deep levels in the lower half of the band gap. It is found that Cus atoms form complexes with one, two, and three hydrogen atoms, with Cus-H and Cus-2H being electrically active. It is noted that the addition of either hydrogen or copper has a similar effect on the deep-level structure of Cus.