Cognitive adversary is a type of adversary which can inject jamming signals over a victim's frequency band while simultaneously monitoring all the network frequency bands for potential countermeasures. Establishing reliable communication without getting detected by such an adversary is a challenging task in wireless security. Under this class of adversaries, a new threat model was recently proposed, wherein the adversary monitors the instantaneous energy of the transmitted symbols over all the frequency bands of the network to detect coun-termeasures. Although a cooperative mitigation strategy exists against such an adversary, such a strategy compromises the rate of the helper nodes in the network as well as incurs additional communication overhead due to preshared secret bits. In this work, we propose a variant of this mitigation strategy to address the above mentioned shortcomings, and present a comprehensive performance analysis on its reliability. We show that our variant enjoys high-rate and low-overhead properties along with comparable error performance as that of the state-of-the-art strategy, however, with higher decoding complexity. On the other hand, we also show that sub-optimal error performance can also be achieved, with error rates decreasing with signal-to-noise-ratio, while maintaining the same decoding complexity as that of state-of-the-art strategy.