High brightness laser radiation of chemical oxygen iodine lasers (COIL) requires resonator types especially adapted to low gain medium and rectangular cavity geometry. For medium energy class lasers, those resonators suffer from small magnification numbers and therefore often imply sophisticated optical concepts. Selected solutions should not inhibit the demands of a field deployment of the laser system. Outside the laboratory additional nonoptical properties like compactness, ruggedness and ease of operation become important. Resonators that enable reliable operation under field conditions should be composed of a reasonable number of optical components and a straightforward architecture. Based on the amplification characteristics of a 10 kW-class COIL, off-axis hybrid resonator configurations are designed and pre-evaluated theoretically. The most promising candidates are technically realized and applied to the DLR-COIL device. The resonators are tested for their alignment sensitivity and brightness parameters. Positive branch and negative branch hybrid resonators are discussed. Particularly, the negative branch hybrid resonator meets the above challenges. A further promising design approach, the multi-pass hybrid resonator, will be depicted within this paper.