Philosophers of science have come to accept that contextual values can play unavoidable and desirable roles in science. This has raised concerns about the need to distinguish legitimate and illegitimate value influences in scientific inquiry. I discuss here four such concerns: epistemic distortion, value imposition, undermining of public trust in science, and the use of objectionable values. I contend that preserving epistemic integrity and avoiding value imposition provide good reasons to attempt to distinguish between legitimate and illegitimate influences of values in science. However, the trust and the objectionable values concerns constitute no good reason for demarcation criteria.