One of the underlying assumptions of classical choice theory is that the presented choice set is the same as what the agent indeed considers while deciding. However, marketing literature provides well-established evidence that consumers do not consider all brands in a given market before making a purchase decision. Instead, they restrict their attention to only a subset of it and then undertake a more detailed analysis of the reduced sets of alternatives. Building on this idea, we model individuals who are able to pay attention to only a subset of the choice problem presented to them. Within this smaller set, a decision maker is rational in the standard sense and she chooses the maximal element with respect to her preference. We show that from the observed behavior we can derive which alternatives individuals pay attention to and according to which preference they maximize.