Individual variations in animal behaviour can be used to describe relationships between different constructs, as well as the underlying neurobiological mechanisms responsible for such variation. In humans, variation in the expression of certain traits contributes to the onset of psychopathologies, such as drug addiction. Addiction is characterised by persistent drug use despite negative consequences, but it occurs in only a sub-population of drug users. Compulsive drug use is modelled in laboratory animals by punishing a drug-reinforced operant response. It has been reported that there is individual variability in the response to punishment, and in this report we aim to further define the conditions under which this variation can be observed. We have previously used footshock punishment to suppress alcohol seeking in an animal model of context-induced relapse to alcohol seeking after punishment-imposed abstinence. Here we present a re-examination of the training and punishment data from a large cohort of rats (n = 499) collected over several years. We found evidence for a bimodal distribution in the response to punishment in alcohol preferring P rats. We only observed this population split when rats received constant shock intensity for three sessions, but not when increasing shock intensity was used. This observation provides evidence for the existence of two distinct groups of rats, defined by their response to punishment, in an otherwise homogeneous population. The implications of this observation are discussed in reference to prior observations using punishment of other addictive drugs (cocaine and methamphetamine), the potential causes of this phenomenon, and with broader implications for the cause of alcohol and drug addiction in humans.