Identifying nonaddictive opioid medications is a high priority in medical science, but μ-opioid receptors (MORs) mediate both the analgesic and addictive effects of opioids. We found a significant pharmacodynamic difference between morphine and methadone that is determined entirely by heteromerization of MORs with galanin Gal1 receptors (Gal1Rs), rendering a profound decrease in the potency of methadone. This finding was explained by the weaker proficiency of methadone in activating the dopaminergic system as compared with morphine and predicted a dissociation of the therapeutic and euphoric effects of methadone, which was corroborated by a significantly lower incidence of self-reports of feeling “high” in methadone-medicated patients. These results suggest that μ-opioid–Gal1R heteromers mediate the dopaminergic effects of opioids. The results further suggest a lower addictive liability of some opioids, such as methadone, due to their selective low potency for the μ-opioid–Gal1R heteromer.