We have investigated a simple yet powerful method for making sharp scanning tunneling microscopy tips of Pt/Ir. It consists of three electrochemical polish/etch steps, not requiring any special micropolishing. The tips, as seen by high-resolution transmission electron microscopy, are sharper than 20 Å. Furthermore, they are smooth, without mini tips and covered with an oxide layer not much thicker than the native one (as seen from a freshly cut wire) when all three steps are applied.