In stochastic acoustic emission, both theory and experiments suggest that the power of the acoustic emission signal is proportional to the source energy. Hence, inference about the power is equivalent to inference about the source energy except for a constant multiple. In this regard, the connection between peaks exceeding a fixed level and the power in random acoustic emission waves is explored when the source energy is an impulse of short duration. Under certain conditions, the peak distribution is sensitive to power changes, determines it and is determined by it. The maximum likelihood estimator of the power from a random sample of peaks- the peak estimator - is more efficient than the maximum likelihood estimator - average sum of squares - from a random sample of the same size of signal values. When evaluated from nonrandom samples, indications are that the peak estimator may still have a relatively small mean square error. A real data example indicates that the left-truncated Rayleigh probability distribution may serve as an adequate model for high peaks.