Carbon capture and storage (CCS) will have an essential role in meeting our climate change mitigation targets. CCS technologies are technically mature and will likely be deployed to decarbonise power, industry, heat, and removal of CO₂ from the atmosphere. The assumption of a 90% CO₂ capture rate has become ubiquitous in the literature, which has led to doubt around whether CO₂ capture rates above 90% are even feasible. However, in the context of a 1.5 °C target, going beyond 90% capture will be vital, with residual emissions needing to be indirectly captured via carbon dioxide removal (CDR) technologies. Whilst there will be trade-offs between the cost of increased rates of CO₂ capture, and the cost of offsets, understanding where this lies is key to minimising the dependence on CDR. This study quantifies the maximum limit of feasible CO₂ capture rate for a range of power and industrial sources of CO₂, beyond which abatement becomes uneconomical. In no case was a capture rate of 90% found to be optimal, with capture rates of up to 98% possible at a relatively low marginal cost. Flue gas composition was found to be a key determinant of the cost of capture, with more dilute streams exhibiting a more pronounced minimum. Indirect capture by deploying complementary CDR is also assessed. The results show that current policy initiatives are unlikely to be sufficient to enable the economically viable deployment of CCS in all but a very few niche sectors of the economy.