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.