One treatment for obstructive sleep apnea is oral appliance therapy during sleep, in which an appliance that covers the upper and lower teeth acts to pull the lower jaw forward, opening the throat passage and allowing for normal breathing. However, oral appliance therapy does not treat sleep apnea effectively in all individuals. In order to identify those individuals for whom oral appliance therapy will work, the study sponsor has developed an investigational device called an auto-titrating mandibular positioner. The device automatically pulls the lower jaw forward in response to respiratory events while the individual sleeps. Study participants will learn the outcome of their sleep tests and will provide feedback on the ease of use of the device.