Limited diffraction beams have a large depth of field and are approximately depth-independent, even if they are produced with a finite aperture. Therefore, they may have applications in medical imaging, tissue characterization, nondestructive evaluation of materials, as well as other physical branches such as optics and electromagnetics. However, limited diffraction beams have larger sidelobes than those of conventional beams at their focuses. A method has been proposed for reducing the sidelobes of limited diffraction beams at the expense of frame rate. In this paper, we study the efficacy of the method when stepwise aperture weighting functions are used to produce the beams. Results show that the method works well with a transducer of only 14 rings and 16 sectors. The transducer has a 25 mm diameter and 3.5 MHz central frequency, and can produce a pulse-echo response that maintains a -6-dB mainlobe width of about 1.83 mm over a depth of field of about 150 mm.