A coyote in a field. (Karen Nichols/AP)

In mid-December, a hunting contest was held in central Arizona for the 11th year in a row. The team that killed the most coyotes won. The event’s name emphasized the goal: It was called the “Santa Slay Coyote Tournament.”

It might have been the contest’s final year. The Arizona Game and Fish Commission is now considering banning Santa Slay and other privately run derbies that target predators and animals typically hunted for their fur. While coyote hunting would remain legal year-round and with no bag limits, a proposed rule would draw the line at doing it for competition.

“We’re not looking for controversial things to get into,” Jim Zieler, the commission’s chairman, said in an interview. “But this is something that we needed to evaluate a little bit closer and make sure we’re…