Voters here chose the three candidates who called themselves "fiscal conservatives" and "common sense decisions-makers."
In unofficial results, incumbent Ryan Buckhannon got 728 votes and newcomers Jimmy Carroll and Jimmy Ward were just one vote apart, at 692 and 691, respectively.
"We're all independent candidates, but we knew we needed to stick together," said Buckhannon. "We're all long-time island residents and we're going to listen to the voters."
For the fourth seat, a runoff may be required between incumbent Michael Loftus (629 votes) and Anne Bauer (615), officials said. Numbers were unavailable for incumbents Brian Duffy and Ralph Piening, but they finished sixth and seventh, candidates said.
Also unavailable was the total number of ballots cast. Each voter could choose up to four candidates.
Carroll said he, Ward and Buckhannon "feel very fortunate. Things are going to change a lot. We're going to have positive government instead of a lot of negativity. This was a tough campaign and there were a lot of things going on."
Poll worker Charles Jones said he was pleased with the turnout, since only four council seats were up for grabs.
"I guess it's because we've had such controversial issues lately," he said, referring to a current issue on how to handle tourist parking.