The invention is based on the discovery that certain self-filleting die attach adhesives are useful in semiconductor die assemblies containing thin die. As used herein, the term “self-filleting” refers to any adhesive that when dispensed and then subjected to suitable cure conditions, will flow and fill up the area between two die or between a die and a substrate while not forming a bulky fillet that can overflow onto the top of the die. In addition, the invention is useful for tight tolerance semiconductor die assemblies, since the fillet from the die-attach adhesives employed in the methods of the invention does not cover bond fingers, thereby causing wire bond yield loss.