Next-generation 76Ge neutrinoless double-beta decay experiments will require an unprecedented ultra-low level of radioactive background. The cryostat, shielding materials, and front-end electronics are a significant source of background. Efforts to improve materials purity are ongoing and analysis techniques are under development to mitigate the few expected remaining backgrounds. Two of these techniques -- detector segmentation and pulse-shape discrimination -- have been implemented for a prototype physically-segmented p-type germanium detector (PSEG) to experimentally quantify background rejection efficacy. The result of applying both cuts is a 90% improvement in the predicted T0n1/2 discovery sensitivity for a PSEG-based next-generation experiment. When considering the practical reality of having to electronically instrument each additional segment, the increased experimental background results in a 19% reduction in the T0n1/2 discovery sensitivity for a PSEG-based nextgeneration experiment. In comparison, using the published background rejection efficacy for a new type of unsegmented germanium detector (p-type point contact -- PPC) resulted in a 168% improvement in the predicted T0n1/2 discovery sensitivity for a PPC-based next-generation experiment. The two active 76Ge neutrinoless double-beta decay collaborations -- MAJORANA and GERDA -- are planning to field some or all segmented germanium detectors. In light of the research presented in this document, these collaborations must consider that the added background associated with segmentation can quickly negate any benefit gained and even reduce the sensitivity of a next-generation 76Ge neutrinoless double-beta decay experiment.