Recent experimental work [Ho et al., J. Acoust. Soc. Am. (to be published)] indicates that replacing the straight-edge top of a noise barrier with a random edge of the same average height can result in improved insertion loss, except at low frequencies. It is thought that the jaggedness reduces the coherence of the sound diffracted off the edge so that the signal amplitude is diminished. These experimental results were obtained in a laboratory using a spark source and defining the maximum peak-to-peak sound pressure at the receiver as the metric. However, because the jagged edge has the effect of increasing the time of duration of sound observed from an impulsive source, it is not clear from the original results that the random-edge barrier reduces the sound energy received. Here the results of a new set of experiments using a similar test setup, but with more rigorous signal analysis are reported. This permits determination of whether the introduction of the randomness reduces the energy received. Additionally, it allows one to determine more precisely the conditions under which the jagged-edge barrier performs worse than a straight-edge barrier.