We present a method for obtaining diffraction/attenuation resistant beams in absorbing media through suitable superposition of ideal zero-order Bessel beams. Such beams keep their resistance to diffraction and absorption even when generated by finite apertures. Although the method is developed for scalar fields, it can be applied to vector wave fields, as well. These new beams have many potential applications, such as in free-space optics, medical apparatus, remote sensing, and optical tweezers. © 2011 IEEE.