In recent weeks, several small pets have been attacked, and some have even been killed - including Ann Kurtz's dog, Jessie, which her daughter found dead in the backyard on Newark Court two weeks ago.
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"He was my dog, he slept on my pillow like a human, so obviously, still, it's been really difficult... it was really traumatizing, to be honest, to find your dog in the backyard, mangled."
Matt Brooks' dog was nearly attacked earlier this year.
"It was probably about 15 feet away from our dog," Brooks said. "(We) made enough ruckus to scare it away, but we were that close to having our own dog as the victim."
Greenwood city officials said they're considering their options, including the possibility of setting traps, though many details still have to be worked out.
One council member told Fox59 News the best option might simply be letting nature run its course.
"As a city, we're looking at every possible means we can to help alleviate problem of coyotes," said council member Thom Hord. "We're receiving a lot of emails and phone calls from people concerned about the coyotes, as well they should be."
Hord said the danger to people was minimal, a concern raised by some during Wednesday night's trick-or-treat hours.
"Coyote attacks on people are very, very, very rare," Hord said. "They won't come up to you, if you're out walking with your children, they won't come to you and grab you. They'll run from you for the most part."
"It's tough," Kurtz said. "I just hope it doesn't happen to anybody else."
Greenwood's council will meet again Nov. 7 and will hear form several experts about how best to proceed.