An anti-rotation key inserts into a pocket formed on an outer surface of a male threaded connector. The key has a lower inner side portion for contact with the base of the pocket. An array of teeth on a lower outer side portion of the key bite into an inner wall of a female threaded connector as the key is forced into the pocket. One of the edges of the key is configured such that a line tangent to the first side edge where it intersects the lower outer side portion will intersect a line tangent to a central portion of the lower inner side portion at an angle less than 90 degrees. Relative motion between the male and female threaded connectors in a loosening direction causes the key to pivot about an engagement of the first side edge with the first side wall and bite more deeply into the inner wall of the female threaded connector.