A common approach in the realization of wavelet-based compressors for ECG signals makes use of truncation methods, whereby wavelet coefficients are truncated (i.e., thrown away) if they're deemed insignificant. A popular truncation strategy applied in these compressors is to truncate based on Energy Packing Efficiency or EPE, which tends to favor coefficients at higher scales because their energy contribution (either in squared or absolute-value sense) is itself insignificant. In this paper, we present four rudimentary truncation strategies to analyze and demonstrate how the choice of truncation strategy can affect the signal in terms of compression ratio (CR) and signal fidelity. Of these, a truncation strategy we call 'ScaleRelativeMAX' is proposed, which exhibits some useful properties for sensitive biomedical applications. Simulation results are presented using representative select ECG records from PhysioNet's database to show that some truncation methods-in particular, our proposed truncation strategy-allows for fine-grained fidelity and CR control than others and offer nearly linear reconstruction error growth as a function of the truncation threshold in comparison to other strategies that are more aggressive in favoring CR over signal fidelity. Such fidelity-first strategies are useful in biomedical communication architectures for emerging Internet-of-Things (IoT) applications that employ compressors to minimize energy transmission costs in Body Area Sensor Networks (BASNs) and similar wearable devices. Such signals carry diagnostic information that are of clinical significance, and whose reconstruction of clinical features should take priority and is in stark contrast to ordinary multimedia class signals, which generally tend to favor CR over signal fidelity.