Opioid peptides and alkaloid drugs such as morphine, mediate their analgesic effects, but also undesired side effects, mostly through activation of the mu opioid receptor which belongs to the G protein-coupled receptor (GPCR) family. A new important pharmacological concept in the field of GPCRs is biased agonism. Two mu receptor ligands, Dmt-c[D-Lys-Phe-Phe-Asp]NH2 (C-36) and Dmt-c[D-Lys-Phe-p-CF3-Phe-Asp]NH2 (F-81), were evaluated in terms of their ability to promote or block mu receptor/G protein and mu receptor/β-arrestin interactions. Using the bioluminescence resonance energy transfer (BRET) assay it was shown that C-36 activated both, G protein and β-arrestin pathways. Incorporation of trifluoromethyl group into the aromatic ring of phenylalanine in the sequence of F-81 led to activation of G-protein pathway rather than β-arrestin recruitment. Opioid cyclopeptide F-81 turned out to be a biased G protein mu receptor agonist. Such biased ligands are able to separate the biological actions of an activated receptor and have the potential to become more effective drug candidates with fewer side effects.