An explosive structure of the fragmentation type includes an outer casing comprising an energy dense explosive material and having an inner surface defining a chamber and means for propagating shock waves across the inner surface from a selected one of at least first and second detonation points within the casing. The explosive structure further includes first means for directing shock waves, propagated from the first detonation point, against at least a selected portion of the inner surface in a first pattern for scoring and weakening the casing along first, segment-defining lines and second means for directing shock waves, propagated from the second detonation point, against the selected portion of the inner surface in a second pattern for scoring and weakening the casing along second, segment-defining lines, the segments of the second pattern being larger than the segments of the first pattern. The explosive structure further includes means for fragmenting the casing along the resulting, segment-defining lines scored in the casing.