Clean energy deployment scenarios typically assume a diverse mix of low-emission generation. However, because of historically low natural gas prices and cost reductions for onshore wind and photovoltaic technologies, recent new capacity deployment, especially in the United States, has come largely from these three generation sources. Here, we quantify competitive cost targets for three less-common zero-emission generation technologies nuclear, concentrating solar, and offshore wind-under a range of future conditions. We determine the cost targets based on the technologies' system value, such that technology value equals or exceeds its cost. Using a capacity expansion model that develops system-wide, economically optimal generation scenarios of the United States power sector, we find that nuclear, concentrating solar, and offshore wind would need to attain levelized cost ranges of $53-84/MWh, $65-91/MWh, and $39-77/MWh, respectively, to achieve 1% additional grid penetration. We refer to this metric as the "required cost," which is a technology's levelized cost of energy needed to achieve a specific penetration level. Higher penetrations lead to lower required costs as lower-cost generation is displaced. We estimate that to reach 10% penetration, the required cost for nuclear declines to $45-76/MWh. Because of resource variability and increased transmission needs for concentrating solar power and offshore wind, even lower costs are needed to reach higher penetrations: required cost ranges to achieve 10% penetration are estimated to be $30-56/MWh and $18-40/MWh for these two technologies respectively. Our analysis informs research and development priorities and the design of policies supporting clean technologies.