Dose-response studies are thought to be a valuable tool to predict the most genetically drug-vulnerable individuals. However, dose-response curves for morphine self-administration have not yet been examined and nor strain differences might be evident. Therefore, this study aimed to define the dose-response curve for morphine self-administration (0.25, 0.5, 1 and 2 mg/kg) in Lewis (LEW) rats and their histocompatible Fischer-344 (F344) rats. In addition, impulsivity has been suggested as one of the genetic factors contributing most to the initiation of drug use. Therefore, the impulsive choice of both rat strains in the presence or absence of the same morphine doses was also analysed. LEW rats self-administered significantly more morphine whatever the dose tested and they exhibited greater basal impulsive choice compared with F344 rats. The F344 strain showed a preference for the dose of 0.5 mg/kg, while any of the doses used had a differential reinforcing effect in the LEW strain. The basal pattern of strain differences in impulsive choice was not affected by morphine administration. These data suggest that the LEW strain has a highly drug-vulnerable phenotype and they point to the strength of impulsivity as a pre-existing behavioural trait that might make this rat strain more vulnerable to the reinforcing effects of drugs and, therefore, to develop addiction.