For sinusoidal beams, minimization of scintillation index is carried out against the displacements parameters. It is found-that x-y asymmetric cosh-Gaussian beam fulfills the requirements of such optimum beam. Our minimization procedure reveals that the optimum beam is achieved by continually focusing it at the chosen propagation length and by further adjusting displacements parameters to be propagation distance dependent. Scintillation index of thus constructed optimum beam is formulated and numerically evaluated., Our graphical comparisons entailing collimated and focused versions of cos-, cosh-Gaussian, annular-Gaussian and Gaussian beams show that the optimum beam yields the lowest scintillations provided that Propagation range is less than or equal to the focusing distance. (C) 2008 Elsevier B.V. All rights reserved.