The apnea-hypopnea index (AHI) plays a major role in determining whether a patient suffers from SAHS, as well as in evaluating the severity of his/her condition. To obtain this index the number of apneas and hypopneas that the patient has experienced during his/her sleep is calculated, and the result is divided by the number of hours of sleep. The standard definitions of apnea and hypopnea require that these events have a minimum temporal span of 10 seconds. Our experience has taught us that some respiratory airflow limitations lasting less than 10 seconds can produce a noticeable effect on the patient's blood oxyhemoglobin saturation (SpO2). In this paper we propose alternative definitions for apnea and hypopnea events that include respiratory airflow limitations with a temporal span between 5 and 10 seconds when they are associated with a drop in SpO2 of at least 3%. Then we compare the AHI calculated using the standard definition and our definition over a database of 40 polysomnograms. For 2 of the 40 patients, the standard AHI clearly underestimates the severity of the patient's condition, while ours does not.