Cost risk analysis (CRA) continues emerging as a noticed decision-analytic framework within climate economics. It introduces the construct of a climate target into an expected utility-based structure and thereby avoids the dynamic inconsistencies of cost effectiveness analyses under uncertainty (i.e. of chance constraint programming). We present three innovations on CRA. They might complete the set of assumptions necessary for CRA as a ‘bridging technology’, before cost benefit analyses can more unequivocally be applied, in view of a currently potentially underdetermined global warming impact function. (i) We modify CRA such that risks below the climate target are taken care of, while still reflecting the specific choice of the target’s numerical value. (ii) This enables us to provide a consistent mechanism of including matured impact modelling components into a further extended CRA, such in the long run, CRA might converge towards cost benefit analysis. (iii) We provide an updating mechanism for including revisions of the science base of the climate target. We conclude from a thereby extended CRA, that a potential lowering of the temperature maxima the 2° target was based on, as suggested by latest paleo records (Westerhold et al. 2020), would not significantly change the temperature target. Hence, the joint science and economics base behind the Paris agreement could be argued to be still intact.