Wireless Body Sensor Nodes (WBSNs) are miniaturized and ultra-low-power devices, able to acquire and wirelessly trans- mit biosignals such as electrocardiograms (ECG) for extended periods of times and with little discomfort for subjects [1]. Energy efficiency is of paramount importance for WBSNs, because it allows a higher wearability (by requiring a smaller battery) and/or an increased mean time between charges. In this paper, we investigate how noise-aware design choices can be made to minimize energy consumption in WBSNs. Noise is unavoidable in biosignals acquisitions, either due to external factors (in case of ECGs, muscle contractions and respiration of subjects [2]) or to the design of the front- end analog acquisition block. From this observation stems the opportunity to apply inexact strategies such as on-node lossy compression to minimize the bandwidth over the energy- hungry wireless link [3], as long as the output quality of the signal, when reconstructed on the receiver side, is not constrained by the performed compression. To maximize gains, ultra-low-power platforms must be employed to perform the above-mentioned Digital Signal Processing (DSP) techniques. To this end, we propose an under-designed (but extremely efficient) architecture that only guarantees the correctness of operations performed on the most significant data (i.e., data most affecting the final results), while allowing sporadic errors for the less significant data.