The beam parameter product is the most important characteristic value of a materials-processing laser. Known formulas lead to expressions that show its relevance to kerf width, depth of focus, and taper. These new expressions are then applied to fiber optic beam delivery. A formula is presented to minimize reflection losses by specifying antireflection coatings with the right spectral and hence angular bandwidth. These optical principles were used in the engineering of two improved processing heads to image the fiber end face onto the workpiece. A welding objective offers 106 mm of free working distance for reliable welding at high power. A cutting objective offers a 0.3-mm spot size with a 400-μm fiber. Both objectives consist of three lens elements only, thus minimizing cost, mass, and reflection losses. They are corrected to transverse aberrations less than 1/5 and 1/20 of a 400-μm fiber core diameter, respectively.