This article examines some unresolved problems about Boudon's concepts of cognitive rationality and rational action. Some classic examples used by Boudon to support his theory have been re-examined as well as its possible application to the case of alternative medicine. The actor's behaviour in certain situations could be hardly called "rational", nevertheless the search for the "a priori" elements leading his thinking and his representation of the situation seems to be a useful approach. Moreover the most common "a prioris" could be identified; the conditions of the actors' interaction and the influence of institutional constraints could be introduced in the "a priori" map. These elements have not always been explicitly considered by Boudon. The beliefs in the alternative medicine represent a case that could be explained by Boudon's theory integrated with the above mentioned elements. In this example the actor's health conditions, the cost-benefit balance of the various therapies, the everyday life interactions and the institutionalised expectations over the therapist's role model a kind of rationality grounded on well-defined "a prioris" in a given situation. In the background a general question still remains without answer: why do some people seem to be guided by a certain kind of "rationality" and some others do not?