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Evidence from several novel opioid agonists and knockout animals suggest that improved opioid therapeutic window, notably for analgesia versus respiratory depression, can be caused by ligand bias downstream of activation of the mu-opioid receptor (MOR) towards G-protein signaling and away from other pathways such as arrestin recruitment. Here, we argue that published claims of opioid bias based on application of the operational model of agonism are frequently confounded by failure to consider the assumptions of the model. These include failure to account for intrinsic efficacy and ceiling effects in different pathways, distortions introduced by analysis of amplified (G-protein) versus linear (arrestin) signaling mechanisms, and non-equilibrium effects in a dynamic signaling cascade. We show on both theoretical and experimental grounds that reduced intrinsic efficacy that is unbiased across different downstream pathways does produce apparent but erroneous MOR ligand bias towards G-protein signaling, and the weaker the G-protein partial agonism the greater is the apparent bias. Experimentally, such apparently G-protein biased opioids have been shown to exhibit low intrinsic efficacy for G-protein signaling when ceiling effects are properly accounted for. Nevertheless, such agonists do display an improved therapeutic window for analgesia versus respiratory depression. Reduced intrinsic efficacy for G-proteins rather than any supposed G-protein bias provides a more plausible, sufficient explanation for the improved safety. Moreover, genetic models of G-protein biased opioid receptors and replication of previous knockout experiments suggest that reduced or abolished arrestin recruitment does not improve therapeutic window for analgesia versus respiratory depression. SIGNIFICANCE STATEMENT: Efforts to improve safety of mu-opioid analgesics has focused on agonists that show signaling bias for the G-protein pathway versus other signaling pathways. This review provides theoretical and experimental evidence showing that failure to properly consider the assumptions of the operational model of bias commonly leads to large distortions and overestimation of actual bias. We show that low intrinsic efficacy is a major determinant of these distortions and pursuit of appropriately reduced intrinsic efficacy should lead development of safer opioids.