<p>Improvements in electronic tag technology have enhanced the ability to monitor the post-release fate of fish and estimate discard mortality rates (<em>DM</em>) under real-world conditions. However, correctly estimating <em>DM</em> requires disentangling the influence of capture-related mortality from natural (background) mortality (<em>M</em>), particularly when <em>M</em> rates are elevated. To accomplish this, many published studies have used an ad hoc and largely arbitrary approach, assuming that all mortality occurring during a finite, non-standard, pre-defined period following release is strictly <em>DM</em>, and all mortality occurring after this period is <em>M</em>. This approach may lead to biased estimates of <em>DM</em>, which we illustrate using a simulation. Here we extend an existing parametric survival model to independently estimate <em>DM</em> and <em>M</em> from electronic tagging data generated by two <em>DM</em> experiments conducted on southern bluefin (<em>Thunnus maccoyii</em>) and yellowfin (<em>Thunnus albacares</em>) tuna, species experiencing contrasting levels of <em>M</em>. In both cases, predation following release was an important cause of mortality that may have been facilitated by capture and discarding, and therefore part of <em>DM</em> or the <em>DM</em> experiment, or may have been natural. Using a multi-model approach based on model fit and biological plausibility, we consider different assumptions for these mortality processes and attempt to account for experimental (tag-induced) mortality. Despite the modest sample sizes of the case studies, we show how our approach can be used to provide bounds on the plausible magnitude of <em>DM</em> in support of possible subsequent fishery management actions such as the imposition of size limits or catch retention policies.</p>