A tip-based approach to shaping surfaces of soluble materials with nanometer-scale control is reported. The proposed method can be used, for example, to eliminate defects and inhomogeneities in surface shape, repair mechanical or laser induced damage to surfaces, or perform 3D lithography on the length scale of an AFM tip. The phenomenon that enables smoothing and repair of surfaces is based on the transport of material from regions of high to low curvature within the solution meniscus formed in a solvent-containing atmosphere between the surface in question and an AFM tip scanned over the surface. Using in situ AFM measurements of the kinetics of surface remodeling on KDP (KH(2)PO(4)) crystals in humid air, we show that redistribution of solute material during relaxation of grooves and mounds is driven by a reduction in surface free energy as described by the Gibbs-Thomson law. We find that the perturbation from a flat interface evolves according to the diffusion equation, where the effective diffusivity is determined by the product of the surface stiffness and the step kinetic coefficient. We also show that, surprisingly, if the tip is instead scanned over or kept stationary above an atomically flat area of the surface, a convex structure is formed, with a diameter that is controlled by the dimensions of the meniscus, indicating that the presence of the tip and meniscus reduces the substrate chemical potential beneath that of the free surface. This allows one to create nanometer-scale 3D structures of arbitrary shape without the removal of substrate material or the use of extrinsic masks or chemical compounds. Potential applications of these tip-based phenomena are discussed.