Thinned arrays are designed to have low average sidelobe levels. The randomness in selecting the elements that are turned on/off to achieve the low sidelobes implies that there are several arrangements of the thinned aperture that have the same or nearly the same average sidelobe level. If the same number of elements are always turned on, but the elements that are turned off change, then the array directivity does not change, but the nulls and sidelobes do. This paper presents a technique for dynamically altering the thinning configuration of a linear array in order place low sidelobe and nulls in desired directions. A set of representative results is reported and discussed to show the effectiveness of the proposed approach.