The pulse-height versus deposited energy response of a single-crystal chemical vapor deposition (scCVD) diamond detector was measured for ions of Ti, Cu, Nb, Ag, Xe, Au, and of fission fragments of 252 Cf at different energies. For the fission fragments, data were also measured at different electric field strengths of the detector. Heavy ions have a significant pulse-height defect in CVD diamond material, which increases with increasing energy of the ions. It also depends on the electrical field strength applied at the detector. The measured pulse-height defects were explained in the framework of recombination models. Calibration methods known from silicon detectors were modified and applied. A comparison with data for the pulse-height defect in silicon detectors was performed.