A dynamic-action, pliable, anatomically conformable bandaging structure for application to an anatomical wound including a pliable, low-rebound, viscoelastic, acceleration-rate-sensitive cushioning expanse which is placeable confrontingly adjacent such a wound, and operatively associated and structurally united with that cushioning expanse, adjustable, pressure-fluid-inflatable structure. An associated methodology features the steps of (a) applying over a wound area a first, dynamic-action bandaging structure in the form of the mentioned cushioning material, (b) by such applying, furnishing dynamic, low-rebound, viscoelastic, acceleration-rate-sensitive pressure-applying behavior, and (c) utilizing the mentioned pressure-fluid-inflatable structure, applying, through the cushioning material, collaborative, dynamic, controlled, contained pressure-fluid action.