Single unit action potentials that are found in extracellular neural recordings are often detected using a threshold. The threshold is usually computed as proportional to the standard deviation of the entire recording. Such thresholds increase with firing rate. Here, the firing rate dependence of "truncation thresholds", which are thresholds that are computed using a different approach, is investigated through simulation. Simulated data are constructed using extracellular recordings from cortical area M1 of awake behaving rats. The findings show that, unlike other thresholds, truncation thresholds decrease in absolute value with firing rate. In this way, the value of these thresholds adapts to weed out the noise depending on the firing rate. The results show that truncation thresholds are better than the alternatives considered here at determining the noise component in extracellular recordings.