Drug self-administration models of addiction typically require animals to make the same response (e.g., a lever-press or nose-poke) over and over to procure and take drugs. By their design, such procedures often produce behavior controlled by stimulus-response (S-R) habits. This has supported the notion of addiction as a "drug habit," and has led to considerable advances in our understanding of the neurobiological basis of such behavior. However, to procure such drugs as cocaine, addicts often require considerable ingenuity and flexibility in seeking behavior, which, by definition, precludes the development of habits. To better model drug-seeking behavior in addicts, we first developed a novel cocaine self-administration procedure [puzzle self-administration procedure (PSAP)] that required rats to solve a new puzzle every day to gain access to cocaine, which they then self-administered on an intermittent access (IntA) schedule. Such daily problem-solving precluded the development of S-R seeking habits. We then asked whether prolonged PSAP/IntA experience would nevertheless produce "symptoms of addiction." It did, including escalation of intake, sensitized motivation for drug, continued drug use in the face of adverse consequences, and very robust cue-induced reinstatement of drug seeking, especially in a subset of "addiction-prone" rats. Furthermore, drug-seeking behavior continued to require dopamine neurotransmission in the core of the nucleus accumbens (but not the dorsolateral striatum). We conclude that the development of S-R seeking habits is not necessary for the development of cocaine addiction-like behavior in rats. Substance-use disorders are often characterized as "habitual" behaviors aimed at obtaining and administering drugs. Although the actions involved in consuming drugs may involve a rigid repertoire of habitual behaviors, evidence suggests that addicts must be very creative and flexible when trying to procure drugs, and thus drug seeking cannot be governed by habit alone. We modeled flexible drug-seeking behavior in rats by requiring animals to solve daily puzzles to gain access to cocaine. We find that habitual drug-seeking isn't necessary for the development of addiction-like behavior, and that our procedure doesn't result in transfer of dopaminergic control from the ventral to dorsal striatum. This approach may prove useful in studying changes in neuropsychological function that promote the transition to addiction.