A shimless aligner for insertion between a machine foot and base to align the foot relative to the base, which foot and base are secured together by a hold-down bolt extending between the foot and base. The aligner includes, a top plate having a slanted bottom surface, a taper wedge having a slanted top surface slidably engaging the slanted bottom surface of the top plate and further having a vertical alignment rod extending substantially laterally, a bottom plate below the taper wedge, and a back plate attached substantially perpendicularly at one end of the bottom plate. For receiving the hold-down bolt, the top and bottom plates have a corresponding hole, while the taper wedge has a slot. Said back plate has a hole for the vertical alignment rod to slidably engage the hole thereby preventing rotation of the taper wedge during vertical alignment operations and preserving bent foot corrections.