This study will compare the effectiveness of the two leading oral appliances (OAs) designs for the treatment of severe obstructive sleep apnea in overweight adults. The effectiveness of OAs has come under question since different designs are combined in evaluating treatment efficacy, for example when comparing them to continuous positive airway pressure Due to the wide range of reported efficacy (53 to 90%), it is of great value to identify the most effective design to guide sleep practitioners and patients.