Broad-band random-phase (BRP) irradiation is one of the beam smoothing techniques for KrF laser drivers. We have introduced this technique into the KrF laser system ASHURA. By one-dimensional (ID) BRP smoothing, the speckle pattern in conventional random-phase irradiation has been removed. Two BRP beams were overlap-focused on the target incoherently. Although the obtained profile is rather smooth, some low-frequency nonuniformity remains. To improve the uniformity, a new technique for two-dimensional (2D) smoothing has been proposed. In this technique, a wedged etalon is used to get angular dispersion to the orthogonal direction to the ID BRP effect. The preliminary experiment has been carried out.