We have found that highly efficient waveform recall is possible in coherent transient systems in which the storage is optically thick. Coherent transients may be used in a variety of information storage and processing applications with advantages over traditional electronic methods. However, it is believed that a serious problem in application of photon echoes in practical systems is the relatively low efficiency of the process. We show in our numerical studies that waveform recall efficiencies greater than unity can be achieved in absorbing media with appropriate choice of absorption length and brief pulse area, even for very weak data pulses. We also present our preliminary experimental results in Barium vapor in which efficiencies of 50% were obtained for both the stimulated and two-pulse photon echoes.