An often-cited reason for studying the process of invasion by alien species is that the understanding sought can be used to mitigate the impacts of the invaders. Here, we present an analysis of the correlates of local impacts of established alien bird and mammal species in Europe, using a recently described metric to quantify impact. Large-bodied, habitat generalist bird and mammal species that are widespread in their native range, have the greatest impacts in their alien European ranges, supporting our hypothesis that surrogates for the breadth and the amount of resources a species uses are good indicators of its impact. However, not all surrogates are equally suitable. Impacts are generally greater for mammal species giving birth to larger litters, but in contrast are greater for bird species laying smaller clutches. There is no effect of diet breadth on impacts in birds or mammals. On average, mammals have higher impacts than birds. However, the relationships between impact and several traits show common slopes for birds and mammals, and relationships between impact and body mass and latitude do not differ between birds and mammals. These results may help to anticipate which species would have large impacts if introduced, and so direct efforts to prevent such introductions.