A set of windows whose normalized half main-lobe widths fall between those of rectangular and the Hanning or Hamming windows, is proposed. These windows are compared with Kaiser's near-optimum zeroth-order Bessel and first-order Bessel windows. The results show that the new windows compare very favourably with Kaiser's windows. The distinct advantage of the windows is their very simple form, similar to that of a Hamming window. As an example of the use of these windows, an estimate of the log power spectrum of a signal consisting of two sinusoidal tones of unequal amplitudes is considered and compared with the estimates using other windows. © 1993 Taylor & Francis Ltd.