  The Liquid Xenon Gamma-Ray Imaging Telescope (LXeGRIT) is a balloon born
experiment sensitive to \g -rays in the energy band of 0.2-20 MeV. The main
detector is a time projection chamber filled with high purity liquid xenon
(LXeTPC), in which the three-dimensional location and energy deposit of
individual \g -ray interactions are accurately measured in one homogeneous
volume. To determine the \g -ray initial direction (Compton imaging), as well
as to reject background, the correct sequence of interactions has to be
determined. Here we report the development and optimization of an algorithm to
reconstruct the Compton scattering sequence and show its performance on Monte
Carlo events and LXeGRIT data.
