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It is shown that, by choosing appropriate values for the parameter a of the generating kernel in constructing P.J. Burt and E.H. Adelson's pyramid for motion estimation (see IEEE Trans. Commun., vol.31, p.337-45, 1983), one can eliminate the operation of the floating point multiplications needed in such a construction and reduce the computational load to the same order as in the case of the mean pyramid. When a is chosen to be 3/8, it is demonstrated, through simulation studies, that the corresponding Burt and Adelson's pyramid does not degrade the performance of motion estimation, as compared to that using kernels giving the best performance, and this pyramid also provides perceptually better motion-compensated images than those provided by the mean pyramid.