Self-leveling pad assemblies are described having novel supports that include backing disks and compensating disks. The backing disks have inner and outer collars on its second surface and a flexible compensating disk supported on the outer collar creating a cavity between the two collars and the two disks. The assemblies self-leveling properties result from the compensating disk's ability to flex or bend into the cavity and allow the sealing and cushion layers to conform to the contour of the instrument's tone hole. Self-leveling pad assemblies according to the present disclosure are particularly useful on woodwind instruments that include flutes, clarinets and the like. The compensating disk, having limited flexibility, provides sufficient support for the pad's sealing surface, maintains an even tension on the pad's skin, has sufficient flexibility to allow the pad's surface to conform to an imperfect tone hole and to seal with only a cursory leveling procedure and reduces the number of tears in the pad's skin resulting from repeated forceful contacts with the tone hole to create a seal and from fluctuations in the skin's moisture content.