In this paper, we consider the physics of slab laser discharges and in particular, the conditions for the avoidance of the alpha-to-gamma discharge instability at high power densities, and their implications for the design of waveguide slab lasers. The specific power extracted from multimode slab lasers has been observed to vary inversely with electrode separation, d and values to 30 kW.m-2 have been achieved. In addition, multi-hundred watt cw power output has been observed at pressures of half an atmosphere without the use of high helium concentrations. For small values of d, the beam profile in the transverse direction is that of a fundamental waveguide mode, so the design of resonators for high quality output beams reduces to a 1-dimensional problem. As a consequence of the low losses associated with hollow waveguide propagation in the transverse direction, it is possible to achieve efficient, high power laser outputs while employing an unstable resonator configuration in the lateral dimension, despite the comparatively low gain of the cw carbon dioxide laser. We report the achievement of high quality laser beams from such resonators at power levels in excess of 1 kW from a sealed diffusion-cooled device. A second design of resonator has been demonstrated, in which a single high order waveguide mode in the lateral (wide) dimension of the slab is selected using a new mode control technique, which is based upon intra-cavity coherent imaging and depends on the exploitation of the Talbot effect. Results obtained with this all-waveguide resonator are presented.