We present a general spectroscopic technique for the computation of the distribution of gap-states (DOS) in amorphous semiconductors from transient photocurrent decay (TPC). The technique assumes trap-limited and is otherwise model-independent. It is valid whether the TPC exhibits anomalous or conventional dispersion, and also works without modification for pre- and post-recombination regions of the decay. A numerical Fourier integral procedure is used to convert the TPC i(t) data to frequency domain spectra I(?). The DOS is then computed using a procedure developed by the authors  for analysis of modulated photocurrent (MPC) data. The method avoids distortions and computational difficulties associated with other TPC analytical techniques. We report on the application of the method to experimental data on a-Si:H, demonstrating the wide energy range of states accessed, and highlighting the observation that the observed long-time power-law TPC decay, normally associated with a featureless exponential state distribution is consistent with structure in the DOS.