An optimised Blackman window that gives better sidelobe attenuation with almost the same mainlobe energy content as the original Blackman window is presented. The new coefficients yield about 10 dB improvement in the first sidelobe level and almost 4.5 dB improvement in the maximum sidelobe level. Coefficients have been obtained to implement Hamming and Blackman windows in the frequency domain. Two schemes for frequency-domain windowing of the above that require no multiplication or stored constants have been suggested.