μ-Opioid receptor agonists provide potent and effective acute analgesia; however, their therapeutic window narrows considerably upon repeated administration, such as required for treating chronic pain. In contrast, bifunctional μ/δ opioid agonists, such as the endogenous enkephalins, have potential for treating both acute and chronic pain. However, enkephalins recruit β-arrestins, which correlate with certain adverse effects at μ- and δ-opioid receptors. Herein, we identify the C-terminus of Tyr-ψ[(<i>Z</i>)CF[double bond, length as m-dash]CH]-Gly-Leu-enkephalin, a stable enkephalin derivative, as a key site to regulate bias of both δ- and μ-opioid receptors. Using <i>in vitro</i> assays, substitution of the Leu<sup>5</sup> carboxylate with amides (NHEt, NMe<sub>2</sub>, N<sup>Cy</sup>Pr) reduced β-arrestin recruitment efficacy through both the δ-opioid and μ-opioid, while retaining affinity and cAMP potency. For this series, computational studies suggest key ligand-receptor interactions that might influence bias. These findings should enable the discovery of a range of tool compounds with previously unexplored biased μ/δ opioid agonist pharmacological profiles.