Systems and related methods stabilize tissue in the oral cavity and airway, e.g., the soft palate/uvula and/or tongue. The systems and methods employ an operative element sized and configured to be fitted to less mobile tissue in the oral cavity. The operative element is further constructed and arranged to interact with more mobile tissue in the airway to stabilize a preferred tissue orientation. The operative element can comprise a suction source sized and configured to draw more mobile tissue toward the suction source. Alternatively, the operative element can comprise a magnetic source sized and configured to magnetically attract material fitted to more mobile tissue in the airway.