An OrthoMTA compacter is made by machining a Ni-Ti alloy wire using tapered helix creep-feed grinding machines. This aim of this study is to find the optimal dressing conditions to sharpen the corner of a cubic boron nitride (CBN) wheel. On the basis of the results of various experiments, it is verified that the most important factors in dressing are the dressing depth and feeding method, whereas the feed rate has less importance for producing a smaller corner R value. The study also finds the optimum dressing depth to reduce the dressing time, a feeding speed and method to stabilize the machining, and the mesh grade for the CBN wheel to make the groove of the compacter deeper.