Defect complexes of copper and hydrogen in silicon were studied in detail by deep-level transient spectroscopy. Floating-zone silicon, both n and p types, which had been copper doped during the growth, was hydrogenated by chemical etching. We determine the electrical parameters of substitutional copper and various copper-related deep levels. The concentration profiles after etching were measured and numerically fitted assuming a successive trapping of hydrogen atoms to substitutional copper. From our data we assign the Cu-related deep levels to different charge states of copper-hydrogen complexes containing one or two hydrogen atoms. For the CuH1 defect we measured deep levels at E-C-0.36 eV and E-V+0.54 eV. The two levels at E-C-0.25 eV and E-V+0.27 eV we assigned to a CuH2 complex. We also have evidence for a neutral complex containing three or more hydrogen atoms. In p-type silicon, the capture radii for hydrogen by the substitutional copper have been determined to be 0.3 nm for the first and second hydrogen atoms and 1.0 nm for a third hydrogen atom. In n-type material these values are found to be higher: 0.7 nm, 0.9 nm, and 1.8 nm, respectively.