Forensic DNA phenotyping (FDP) is an emerging technology that seeks to make probabilistic inferences regarding a person's observable characteristics ("phenotype") from DNA. The aim is to aid criminal investigations by helping to identify unknown suspected perpetrators, or to help with noncriminal missing persons cases. Here we provide results from the analysis of 36 interviews with those who have a professional stake in FDP, including forensic scientists, police officers, lawyers, government agencies and social scientists. Located in eight EU countries, these individuals were asked for their views on the benefits and problems associated with the prospective use of FDP. While all interviewees distinguished between those phenotypic tests perceived to either raise ethical, social or political concerns from those tests viewed as less ethically and socially problematic, there was wide variation regarding the criteria they used to make this distinction. We discuss the implications of this in terms of responsible technology development.