A Laplace defect spectrometer (LDS) was investigated for use in decomposition of non-exponential transients. The system was tested by measuring known multi-exponential transients generated by RC circuits and applied to the study of non-exponential transients resulting from electron emission from Sn-related DX centers and hole emission from Fe-related deep accepters. The non-exponential transients were investigated under different conditions and related to the alloy random effect. Their LDS spectra exhibited several well-resolved sharp peaks that were assigned to the fine structures of the two DX centers and the Fe-related deep accepters, respectively, after comparison with DLTS observations. The activation energies of the fine structures were determined by linear fitting of the slopes of temperature dependences of electron and hole emission rates. The results show that the LDS is useful for investigation of deep-level fine structures.