This invention is a substantial improvement/development of a novel coherent combining approach described in a recently filed patent application on N2 times energy enhancement of periodically pulsed signals. Combining of periodically pulsed signals, as described in this filed patent application, is associated with significant practical limitations on resonant-cavity linear combiner length and finesse, making the use of linear beam combiners for achieving high pulse energies impractical. In the course of ongoing experimental study of this technique we came to a realization that a significant improvement in the technique can be achieved if we use pulse bursts instead of strictly periodically pulsed signals. In fact, this new approach can be applied even to a solitary pulse burst. Implementation of this new approach requires an additional inventive step – requires adding of amplitude modulators into each parallel signal path, and applying specific amplitude modulating waveforms onto each to produce channel-specific pulse bursts in each parallel channel. These parallel signals are then combined into a single beam using a properly configured combining resonant cavity. This enables use of short cavity lengths with low finesse, as well as low pulse-repetition rates, thus making linear beam combiners for achieving high-energy pulses practical. Resonant combining cavities have in principle unlimited capacity for high power and high-energy handling, unlike nonlinear combining techniques disclosed in the recently filed disclosure.