Abstract: The microscopic selection mechanisms of single-layer island shapes in Pt(111) homoepitaxy with or without minute amounts of CO adsorbate have been investigated theoretically. For clean growth, only triangular islands of a fixed orientation are obtained within a wide range of growth temperatures, with the orientation uniquely determined by a disparity in the rates of atom supply to an island corner site from the two island edges defining the corner. This novel picture is further corroborated by growth predictions in the presence of CO, whose preferential decoration of one type of the island edges reverses the intrinsic rate disparity for atom supply, thereby inverting the island orientation.