There has long been need for a behavioural intervention that attenuates cue-evoked drug-seeking, but the optimal method remains obscure. To address this, we report three approaches to extinguish cue-evoked drug-seeking measured in a Pavlovian to instrumental transfer design, in non-treatment seeking adult smokers and alcohol drinkers. The results showed that the ability of a drug stimulus to transfer control over a separately trained drug-seeking response was not affected by the stimulus undergoing Pavlovian extinction training in experiment 1, but was abolished by the stimulus undergoing discriminative extinction training in experiment 2, and was abolished by explicit verbal instructions stating that the stimulus did not signal a more effective response-drug contingency in experiment 3. These data suggest that cue-evoked drug-seeking is mediated by a propositional hierarchical instrumental expectancy that the drug-seeking response is more likely to be rewarded in that stimulus. Methods which degraded this hierarchical expectancy were effective in the laboratory, and so may have therapeutic potential.