The study of rational queueing has a long and distinguished history focused on individuals' preference to avoid waiting. Surprisingly, there are settings in which some potential arrivals (which we also refer to as requests) derive utility from waiting and disutility from service. Our primary example is the U.S. affirmative asylum process. In this context, applicants obtain a work permit while waiting for an asylum interview; hence, if the (expected) wait is long enough, then even an applicant who knows that their application will be denied and lead to deportation proceedings, may find it in their interest to apply and thus benefit from legally working during the wait. Similar dynamics could occur in other settings like content moderation in social networks.