A set of windows, whose normalised main lobe widths fall between those of Hamming and the sum-cosine window, are developed. The windows are compared with Kaiser's near optimum zeroth-order Besssl windows. The results show that the new windows yield 4 to 9 dB improvement in the first sidelobe gain, and the improvement in maximum sidelobe gain varies from 2·8 to –085 dB, compared with that of Kaiser windows. The energy in the main lobe of Kaiser windows is at most 0·005% larger than that of the new windows. The distinct advantage of the windows is their very simple form, similar to that of a Hamming window. © 1975, The Institution of Electrical Engineers. All rights reserved.