With personalisation becoming more prevalent, it can often be useful to be able to infer additional preferences from input user preferences. Preference inference techniques assume a set of possible user preference models, and derive inferences that hold in all models satisfying the inputs; the more restrictive one makes the set of possible user preference models, the more inferences one gets. Sometimes it can be useful to have an adventurous form of preference inference when the input information is relatively weak, for example, in a conversational recommender system context, to give some justification for showing some options before others. This paper considers an adventurous inference based on assuming that the user preferences are lexicographic, and also an inference based on an even more restrictive preference model. We show how preference inference can be efficiently computed for these cases, based on a relatively general language of preference inputs.