Four dogs have been found beaten in the head and shot to death in rural southern Idaho, authorities said on Thursday, adding to the mysterious disappearance and killing of dozens of dogs that has left residents in that area on edge.

Examinations showed that the German Shepherd mixes, whose carcasses had been dumped in a pile off a highway south of Twin Falls, had been bludgeoned and shot in the head, said Gary Trostel, deputy with the Twin Falls County Sheriff's Office.

"We didn't know until today how they had died: poisoned or shot or what. We knew it was some type of head trauma the way the eyes bulged out and with all the bleeding," Trostel said.

Animal control officers reported last month that roughly 30 dogs had gone missing since November in Twin Falls and nearby communities in a farming region known as the Magic Valley.

A German shepherd discovered by hikers last month in an area known as the Devil's Corral in neighboring Jerome County appeared to have suffered what animal control officers called a "ritualistic execution" in which its head was crushed with rock and its carcass covered with a purple cloth.

Trostel said an examination of that dog showed it had been beaten and shot in the head.

The Humane Society of the United States is offering a $5,000 reward for information leading to a conviction in the dog's death. It was unclear if that dog's death was related to the other disappearances and killings.

Trostel said pet owners in the area are in a state of "constant concern". He said residents were being urged to report any stalking or disappearance of pets and to prevent their dogs from roaming.

"We're staying on it and working with what leads we have. We know something is going on but we don't know what it all means. We're trying to find out," said Trostel.

No one has claimed the dead dogs. The carcasses show no signs that the animals had been used for dog fighting, which is illegal in Idaho, Trostel said.