We have compared the ability of a number of μ-opioid receptor (MOPr) ligands to activate G proteins with their abilities to induce MOPr phosphorylation, to promote association of arrestin-3 and to cause MOPr internalization. For a model of G protein-coupled receptor (GPCR) activation where all agonists stabilize a single active conformation of the receptor, a close correlation between signaling outputs might be expected. Our results show that overall there is a very good correlation between efficacy for G protein activation and arrestin-3 recruitment, whereas a few agonists, in particular endomorphins 1 and 2, display apparent bias toward arrestin recruitment. The agonist-induced phosphorylation of MOPr at Ser(375), considered a key step in MOPr regulation, and agonist-induced internalization of MOPr were each found to correlate well with arrestin-3 recruitment. These data indicate that for the majority of MOPr agonists the ability to induce receptor phosphorylation, arrestin-3 recruitment, and internalization can be predicted from their ability as agonists to activate G proteins. For the prototypic MOPr agonist morphine, its relatively weak ability to induce MOPr internalization can be explained by its low agonist efficacy.