In regards to psychoanalysis, I think one can say that perfectionism is not an issue, rather it is a symptom of a true issue lying underneath, which can be linked to an unconscious image of an ideal self which must be perfect in order to protect the individual from his or her own insecurities, in a way, to overcompensate perceived internal imperfections which symbiotically exchange psychological energy with the spoken insecurities as well. However, since the demands of the ideal image cannot be met perfectly in every attempt, this defense mechanism in itself is likely to create new insecurities, which are usually projected to the outside world via externalization.
I think the answer to overcoming perfectionism lies in solving the possible internal conflicts lying underneath it.
But how can we solve those conflicts?
I think you should start by asking yourself the question; "What am I trying to hide from myself and others by trying to achieve perfection seemingly impossible even to my own eyes?" Perhaps, what you truly seeking is not perfection, but to cover something much more flawed to you by trying to mold perfection. Speaking of conflicts again, reading about their nature would sure help to a point, but personally my opinion is focused upon making the idealized self image conscious, thus we'll able to see what conflicts are hidden by it, mostly, we create that image to overcome the anxiety created by these conflicts, but then, things may get out of hand and we may start to satisfy the desires of the idealized self image, which we illusorily think as our own wishes and wants. Only by making that ideal image conscious, we can realize what we truly want and what we truly not want and can move accordingly and freely.
I hope this helps.