Increased allocation of behaviour to substance abuse at the expense of personal and social rewards is a hallmark of addiction that is reflected in several of DSM-5 criteria for diagnosis of substance use disorder. Previous studies focused on refining the self-administration (SA) model to better emulate an addictive state in laboratory animals. Here, we employed concurrent SA of sucrose pellets and morphine as two competing natural and drug rewards, respectively, to validate the feasibility of capturing pathological behavioural allocation in rats. A custom-made three-lever operant chamber was used. With one active and one inactive lever presented, rats were trained to self-administer morphine (0.5mg/kg/infusion; 2h/day) under a fixed-ratio 1 (FR-1) schedule until a stable response was achieved. Next, they were trained to self-administer morphine in the presence of a third lever dispensing sucrose pellets (20 mg) under FR-1. Concurrent morphine-sucrose SA sessions (2h/day) were continued until stable morphine taking behaviour was re-established. In another experiment, rats first established stable sucrose pellet SA (2h/day, FR-1) and then were trained to take morphine (0.5mg/kg/infusion; 2h/day). Subsequently, all rats underwent extinction training, in which morphine was replaced with saline while sucrose pellets were still available upon lever pressing, followed by cue-induced reinstatement of morphine seeking behaviour. Results showed that rats retained morphine SA when sucrose pellets were also available, but they showed binge-like sucrose intake when morphine was removed during the extinction sessions. However, morphine SA did not develop in rats that had previously established sucrose pellet SA. In conclusion, morphine SA developed even in the presence of a potent competing nondrug reward in rats. Adding an effort-based contingent delivery of a natural reward to the standard SA model, this protocol may provide an improved model of drug addiction in laboratory animals.