An elastic assembly for absorbent garments having a first carrier layer, a second carrier layer, and an elastic layer attached between the first and second carrier layers to impart elasticity to an elasticized portion of the elastic assembly. The elastic layer is made of elastic strands having a decitex of about 600 or less. The elastic strands are arranged generally in parallel with one another and with a spacing of about 1 to about 10 elastic strands per centimeter. The elasticized portion of the elastic assembly has a thickness of about 2.6 mm or less at a pressure of 0.05 p.s.i. and about 8 or more corrugations per centimeter when in an elastically relaxed state. The first and second carrier layers are attached to one another in the elasticized portion substantially only by a coating of adhesive on the elastic strands. Absorbent garments incorporating the elastic assembly and a method of making the elastic assembly are also provided.