A cull of the animals, agreed by Scottish Borders Council in July looks set to get underway in the coming weeks.
That move comes after residents complained about the overwhelming number of rabbits running around the cemetery and wreaking havoc on graveside flowers, despite the installation of rabbit-proof fencing.
Jedburgh councillor Sandy Scott told the community council’s Tuesday meeting: “The gates to the cemetery have been off for repair works but will be going back on shortly.
“Once the gates are back in place, we will carry out final checks then arrange for Surekill to come in and play their part, which is to euthanise the bunnies.”
Though the rabbits’ days look to be numbered, the town’s community council is having less success when it comes to dealing with the town centre’s pigeon problem.
Community councillor Graham Hayward is calling for a pigeon cull, claiming the birds’ mess is proving troublesome for buildings in the town centre, and he has accused Scottish Borders Council environmental health officers of ignoring the issue.
“He has not spoken to the people he said he was going to,” he said on Tuesday.
“I find it difficult to understand why the council is not prepared to do anything about it. We are getting nowhere.
“Environmental health really needs to push this.”
Although Jedburgh councillor Jim Brown agreed that there was a “definite pigeon problem” in the town, he suggested it is not a job for environment health. He said: “There is one building in particular that is a breeding source for these birds.
“The council has more or less agreed that until we manage to block off the source of the pigeons, behind the Spread Eagle Hotel, we are unable to do very much about it.
“That has to be done with the agreement of the owner as it is private property.”
Mr Scott added: “This has been an ongoing situation for some time. I don’t know what we, as a council, can do about it.”
And his colleague Scott Hamilton warned: “Anything involving environmental health concerns can be a slow process. I’d suggest you may have more luck speaking to the property owner in question in person.”