Why is an elbow dislocation done under anesthetic?

Reducing the elbow, putting it back into place, can be very painful so that's one reason for the anesthetic. The other reason is that when someone is under anesthetic, their muscles relax, allowing the doctor to manipulate the elbow back into place without fighting muscles that are resisting it.

Reference: 

Roger P. van Riet. Elbow dislocations. In Current Orthopaedic Practice. November 2008. Vol. 19. No. 6. Pp. 616-620.

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