Adenotonsillar hypertrophy is the most common reason for children to have sleep disordered breathing (SDB). Even though adenotonsillectomy improves sleep apnea in children, 20-40% of children will still have persistent SDB. Drug Induced Sleep Endoscopy (DISE) is a tool that dynamically evaluates the upper airway during simulated sleep. It identifies sites of upper airway obstruction and/or collapse. It is used to predict which children will get better if their tonsils and adenoids are removed, and which children have other reasons for SDB. DISE is done during a state of simulated sleep. Different anesthetic medications are currently being used. However, there is no identified ideal anesthetic medication to simulate natural sleep. Propofol and Dexmedetomidine are the most frequently used, either alone or in combination with other medications. The aim is to perform a head-to-head study comparing those 2 commonly used regimens. The investigator would like to learn how the anesthetic medication affects performing the procedure and how well our patients tolerate it. This helps us identify an ideal regimen that can be a standardized DISE protocol in the pediatric population in the future. Our objective is to determine which anesthetic regimen, Dexmedetomidine or Propofol, is safer and more efficacious. This will be a randomized controlled trial at the University of Iowa Stead Family Children's Hospital. Children with sleep disordered breathing will undergo DISE and subsequent surgical procedure based on the level of obstruction found during DISE. Via randomization the child will be preselected to have a specific anesthetic for the procedure, either Dexmedetomidine or Propofol. The investigator will record information related to the medications used, the vital signs, the ability to perform DISE fully, the findings seen on DISE and the surgery performed. Consent will be obtained from the legal guardian or parent with legal authority to consent.