Global emissions scenarios play a critical role in the assessment of strategies to mitigate climate change. The current scenarios, however, are criticized because they feature strategies with pronounced overshoot of the global temperature goal, requiring a long-term repair phase to draw temperatures down again through net-negative emissions. Some impacts might not be reversible. Hence, we explore a new set of net-zero CO2 emissions scenarios with limited overshoot. We show that upfront investments are needed in the near term for limiting temperature overshoot but that these would bring long-term economic gains. Our study further identifies alternative configurations of net-zero CO2 emissions systems and the roles of different sectors and regions for balancing sources and sinks. Even without net-negative emissions, CO2 removal is important for accelerating near-term reductions and for providing an anthropogenic sink that can offset the residual emissions in sectors that are hard to abate. Current emissions scenarios include pathways that overshoot the temperature goals set out in the Paris Agreement and rely on future net negative emissions. Limiting overshoot would require near-term investment but would result in longer-term economic benefit.