The major defects of the Woodward-Lawson method of shaped pattern synthesis (lack of control over side lobes and ripple, and high dynamic range ratios) can be overcome by perturbing the field samples weighting the component sin(Nx)/sin(x) beams. If a real field is not necessary, further improvement (especially as regards dynamic range ratio) can be achieved by optimizing the phases of the coefficients of the component beams. These procedures are illustrated by linear arrays producing a symmetric flat-topped beam and a cosecant squared pattern.