Nicotine is thought to underlie the reinforcing and dependence-producing effects of tobacco-containing products. Nicotine supports self-administration in rodents, although measures of its reinforcing effects are often confounded by procedures that are used to facilitate acquisition, such as food restriction, prior reinforcement training, or response-contingent co-delivery of a naturally reinforcing light. This study examined whether rats acquire nicotine self-administration in the absence of these facilitators. A new mathematical modeling procedure was used to define the criterion for acquisition and to determine dose-dependent differences in rate and asymptote levels of intake. Rats were trained across 20 daily 2-h sessions occurring 6 days/week in chambers equipped with active and inactive levers. Each active lever press resulted in nicotine reinforcement (0, 0.015, 0.03, 0.06 mg/kg, IV) and retraction of both levers for a 20-s time out, whereas inactive lever presses had no consequences. Acquisition was defined by the best fit of a logistic function (i.e., S-shaped) versus a constant function (i.e., flat line) for reinforcers obtained across sessions using a corrected Akaike information criterion (AICc) as a model selection tool. The results showed an inverted-U shaped function for dose in relation to the percentage of animals that acquired nicotine self-administration, with 46% acquiring at 0.015 mg/kg, 73% at 0.03 mg/kg, and 58% at 0.06 mg/kg. All saline rats failed to acquire as expected. For rats that acquired nicotine self-administration, multiple model comparisons demonstrated that the asymptote (highest number of reinforcers/session) and half learning point (h; session during which half the assymptote had been achieved) were justified as free parameters of the reinforcers/session function, indicating that these parameters vary with nicotine dose. Asymptote exhibited an inverted U-shaped function across doses and half learning point exhibited a negative relationship to dose (i.e., the higher the dose the fewer sessions to reach h). These findings suggest that some rats acquire nicotine self-administration without using procedures that confound measures of acquisition rate. Furthermore, the modeling approach provides a new way of defining acquisition of drug self-administration that takes advantage of using all data generated from individual subjects and is less arbitrary than some criteria that are currently used.