Inappropriate emergency admissions create overcrowding and may reduce the quality of emergency care. In Italy, overcrowding is further exacerbated by patients who use emergency admissions as a shortcut to avoid the general practitioner (GP) gateway. In this paper, we investigate access to emergency departments (EDs) by patients with non-severe medical conditions and their willingness to wait. Population data for ED accesses in Liguria (an Italian administrative region) in 2016 were used to estimate the number of strategic accesses and waiting time elasticities of low-severity patients. Our results show that the practice of using EDs to skip gatekeeping is a serious problem. The percentage of patients who engage in such practice vary from 8.7 to 9.9% of non-urgent patients; they generally prefer to access more specialized hospitals, especially during weekdays, when GPs are available, but hospitals run at full capacity. Strategic patients are usually much younger than average. From a policy point of view, our results show that long waits may discourage "genuine" patients rather than strategic ones. It is necessary to develop a system to improve access to patients mainly requiring specialist care, along with enhancing the management of diagnostic examinations through primary care.