A simple window that yields 6 dB improvement in the first sidelobe gain, with almost no loss in the maximum sidelobe gain, compared with that of Kaiser's near optimum zeroth-order Bessel window, is developed. The main-lobe energy of Kaiser's window is about 0·00078% more than that of the new window. The distinct advantage of the window is its very simple form similar to that of a Hamming window. © 1974, The Institution of Electrical Engineers. All rights reserved.