Abstract The 2 °C and 1.5 °C temperature targets of the Paris Agreement can be interpreted as targets never to be exceeded, or as end-of-century targets. Recent literature proposes to move away from the latter, in favour of avoiding a temperature overshoot and the associated net negative emissions. To inform this discussion, we investigate under which conditions avoiding an overshoot is economically attractive. We show that some form of overshoot is attractive under a wide range of assumptions, even when considering the extra damages due to additional climate change in the optimisation process. For medium assumptions regarding mitigation costs and climate damages, avoiding net negative emissions leads to an increase in total costs until 2100 of 5% to 14%. However, avoiding overshoot only leads to some additional costs when mitigation costs are low, damages are high and when using a low discount rate. Finally, if damages are not fully reversible, avoiding net negative emissions can even become attractive. Under these conditions, avoiding overshoot may be justified, especially when non-monetary risks are considered.