A modified configuration of the NRD leaky wave antenna is presented. A tunable aperture is introduced at the radiating open end. The taper in the antenna amplitude distribution (required for sidelobe control) is easily achieved by changing the height of the aperture instead of positioning the dielectric slab. This results in the easy design of such an antenna and the reduction of the requirement on the flexibility of the dielectric slab. Numerical results show that when the height of the aperture is appropriately chosen, the phase constant is almost independent of the distance between the right-hand dielectric-to-air interface and the open end.