Self-organized pattern formation has been previously observed in cathode boundary layer discharges (CBLDs) in high-purity xenon gas at pressures ranging from about 60 Torr to atmospheric pressure. However, certain modes predicted by the COMSOL multiphysics simulation were never observed. In this paper, using the same reactor design, we managed to fine tune the discharge current into regions that were not fully explored before. Two new self-organized patterns were observed, at the verge of the extinguishing of the self-organization. One pattern was a perfect ring that was detached from the dielectric walls. The other pattern was a series elongated spots arranged along a circle. Both patterns were preferably observed at pressures ranging from 60 to 120 Torr. The observation of these patterns may open up new discussions to the self-organized pattern formation in CBLD in xenon.