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Comparative extinction risk analysis—which predicts species extinction risk from correlation with traits or geographical characteristics—has gained research attention as a promising tool to support extinction risk assessment in the IUCN Red List of Threatened Species. However, its uptake has been very limited so far, possibly because existing models only predict a species' Red List category, without indicating which Red List criteria may be triggered. This prevents such approaches to be integrated into Red List assessments. We overcome this implementation gap by developing models that predict the probability of species meeting individual Red List criteria. Using data on the world's birds, we evaluated the predictive performance of our criterion‐specific models and compared it with the typical criterion‐blind modelling approach. We compiled data on biological traits (e.g. range size, clutch size) and external drivers (e.g. change in canopy cover) often associated with extinction risk. For each specific criterion, we modelled the relationship between extinction risk predictors and species' Red List category under that criterion using ordinal regression models. We found criterion‐specific models were better at identifying threatened species compared to a criterion‐blind model (higher sensitivity), but less good at identifying not threatened species (lower specificity). As expected, different covariates were important for predicting extinction risk under different criteria. Change in annual temperature was important for criteria related to population trends, while high forest dependency was important for criteria related to restricted area of occupancy or small population size. Our criteria‐specific method can support Red List assessors by producing outputs that identify species likely to meet specific criteria, and which are the most important predictors. These species can then be prioritised for re‐evaluation. We expect this new approach to increase the uptake of extinction risk models in Red List assessments, bridging a long‐standing research‐implementation gap. [ABSTRACT FROM AUTHOR]