The electrical compensation processes of high resistivity CdTe is controlled by deep levels.We have characterized the electrical activity of deep traps by means of three different and complementary spectroscopic methods: photoinduced current transient spectroscopy, surface photovoltage spectroscopy, and space charge limited current analyses. The aim is twofold: to achieve a thorough characterization of the deep trap properties and to assess the potentiality and limitations of the three experimental techniques by a cross correlation of the results obtained with each one of them. We have obtained a direct quantitative estimate of the major deep trap concentration, and we have assessed the sensitivity limit in deep-level detection for surface photovoltage spectroscopy.