Discovering a new species; what kind of evidence is good enough?

Well, the actual animal in hand is usually sufficient. Scientists are still discovering new species (unknown to science, if not to the local residents) on a regular basis. For some reason, it is biologists making these finds, not cryptozoologists, who seem to spend more time either chasing after or perpetrating hoaxes rather than finding real evidence for unknown animals. While a large primate living in North America would be an amazing discovery, the fact that no one has found any definitive evidence in the form of a body, bones, DNA, or even fossil evidence would seem to indicate that the probability of it's existence is close to zero. The real animals still being discovered are fascinating enough.
 
Photo credit; Durrell Wildlife Conservation Trust