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We present a novel concept of a finite-aperture tapered unstable resonator laser based on two distributed Bragg reflectors at the rear and front facets with different lateral widths. An analysis of the passive resonator, as well as a spatiotemporal simulation of the active device, is presented. A variation of the ratio between the widths of both Bragg reflectors changes the losses of the lateral modes differently, leading to certain geometries with good modal discrimination and beam quality. The principle of operation is demonstrated by fabrication and experimental characterization of a first-generation of device.