In order to convince both policy makers and the general public to engage in climate change mitigation activities, it is crucial to communicate the inherent risks in an effective way. Due to the complexity of the system, mitigation activities cannot completely rule out the possibility of the climate reaching a dangerous tipping point but can only reduce it to some unavoidable residual risk level. We present an online experiment based on a sample of US citizens and designed to improve our understanding of how the presence of such residual risk affects the willingness to invest into climate change mitigation. We found that, far from reducing them, the presence of residual risk actually increases investments into mitigation activities. This result suggests that scientists and policy makers should consider being more transparent about communicating the residual risks entailed by such initiatives.