Opioid drugs are potent analgesics that mimic the endogenous opioid peptides, endorphins and enkephalins, by activating the μ-opioid receptor. Opioid use is limited by side effects, including significant risk of opioid use disorder. Improvement of the effect/side effect profile of opioid medications is a key pursuit of opioid research, yet there is no consensus on how to achieve this goal. One hypothesis is that the degree of arrestin-3 recruitment to the μ-opioid receptor impacts therapeutic utility. However, it is not clear whether increased or decreased interaction of the μ-opioid receptor with arrestin-3 would reduce compulsive drug-seeking. To examine this question, we utilized three genotypes of mice with varying abilities to recruit arrestin-3 to the μ-opioid receptor in response to morphine in a novel longitudinal operant self-administration model. We demonstrate that arrestin-3 knockout and wild type mice have highly variable drug-seeking behavior with few genotype differences. In contrast, in mice where the μ-opioid receptor strongly recruits arrestin-3, drug-seeking behavior is much less varied. We created a quantitative method to define compulsivity in drug-seeking and found that mice lacking arrestin-3 were more likely to meet the criteria for compulsivity whereas mice with enhanced arrestin-3 recruitment did not develop a compulsive phenotype. Our data suggest that opioids that engage both G protein and arrestin-3, recapitulating the endogenous signaling pattern, will reduce abuse liability.