We study the lateral and vertical manipulations of single Ag and Cu atoms on the Ag(111) surface with the Cu single-atom and trimer-apex tips using molecular statics simulations. The reliability of the lateral manipulation with the Cu single-atom tip is investigated, and compared with that for the Ag tips. We find that overall the manipulation reliability (MR) increases with the decreasing tip height, and in a wide tip-height range the MR is better than those for both the Ag single-atom and trimer-apex tips. This is due to the stronger attractive force of the Cu tip and its better stability against the interactions with the Ag surface. With the Cu trimer-apex tip, the single Ag and Cu adatoms can be picked up from the flat Ag(111) surface, and moreover a reversible vertical manipulation of single Ag atoms on the stepped Ag(111) surface is possible, suggesting a method to modify two-dimensional Ag nanostructures on the Ag(111) surface with the Cu trimer-apex tip. (C) 2011 Elsevier B.V. All rights reserved.