The lithium ion drift method produces detectors with a highly but not perfectly compensated intrinsic region. The amount of fixed space charge left in the compensated layer and its dependence on drift and clean-up parameters is of great practical interest. The imperfect compensation is mainly due to the presence in the compensated layer of thermally generated electron-hole pairs swept apart by the voltage applied to the detector during drift. A theoretical model is developed which takes into account the influence on the fixed space charge of mobile carrier generation and recombination. When recombination of free electrons and holes is negligible the theory predicts the formation of linear space charge gradients. When recombination is strong a constant space charge throughout a large part of the compensated layer may result. The theoretical calculations are compared with experimental findings. The influence of space charge on detector performance is discussed.