Certain aspects of the methodology of genetic algorithms for global structural optimization of clusters were studied. Through systematic investigations of Lennard-Jones clusters with up to 100 atoms, several modifications were made to the genetic algorithm introduced by Deaven and Ho [Phys. Rev. Lett. 1995, 75, 288]. These modifications result in improved efficiency of the search procedure and in certain cases lead to determination of globally optimal structures that previous genetic algorithm studies have not found. The modifications include the following : twinning mutations, add-and-etch processes where a cluster of a given number of atoms is grown beyond that size and subsequently etched, and seeding of the initial parental population with selected structural motifs, in conjunction with randomly chosen configurations.