Invasive species can be a major threat to biodiversity and economy. Given the large number of introduced invasive species and the limited resources available, a rigorous assessment of the potential impact of these species is of vital importance for prioritizing management programs. Often, general scoring systems in which certain criteria are used to assess the impact of an invader along several impact categories are applied to obtain a ranking of troublesome invaders. Likewise, Kumschick and Nentwig (2010) provided a first categorization of invasive bird impacts in Europe, and argued that several invasive birds should be eradicated because of the threat they pose to biodiversity. This is surprising, as recent reviews suggest that there is little evidence that invasive birds strongly impact biodiversity. We therefore re-evaluated this risk assessment. We found that in the majority of cases, the evidence presented to support impact claims is weak, as they are generally not based on direct scientific research but on often anecdotal observations relating to small areas only. Moreover, even if all claims would materialize, this does not necessarily justify a call for eradication. Previous experiences with eradications have learnt that a feasibility study, encompassing all aspects of biological invasions (including public opinion and possible benefits of the invader) is critical for the achievement of any strategy against invasive species. This is essential, as ill-conceived calls for eradication could result in a public backlash, causing funding agencies and managers to shy away from the problems posed by invasive species.