Convenience Euthanasia

One of the biggest ethical dilemmas that veterinarians must face is
convenience & euthanasia. Veterinarians tend to gravitate to one side
(refuse to perform) or the other (willingly perform), however, some remain in the middle and
determine whether or not they will perform euthanasia on a case-by-case basis. Among
those that refuse to perform state that it is against the code of ethics to euthanize a healthy
animal. Those that willingly perform claim that if they don't, someone else will,
whether it is another veterinarian or a shelter, or worse yet they fear the animal will be
dumped/abandoned.
This is a difficult prompt, as there is no hard science to validate either stance, only scenarios
and statistics to support. As such, this is more or less an ethical prompt. The questions is: if
you were a veterinarian, would you or would you not perform convenience euthanasia? If
your answer is not definitive, what would your criteria be for choosing whether or not to
perform?