Updated: 11:13 p.m.

It appears Alaska Sen. Lisa Murkowski has pulled off the impossible. As write-in ballot counting was completed Tuesday night, Murkowski finished ahead of Republican Joe Miller by more than 10,000 votes, with just a “very small number” of overseas ballots left to count, according to the state Division of Elections.

Murkowski now has 100,868 votes to Miller’s 90,448, plus 20 write-in votes for the Republican. Murkowski’s lead includes 8,153 votes that were challenged by the Miller campaign but were awarded to Murkowski.

State Division of Elections Director Gail Fenumiai judges votes based on voter intent — that voters don’t necessarily need to spell “Lisa Murkowski” exactly right — and ended up awarding most of the ballots Miller challenged to Murkowski. Miller successfully challenged 2,010 ballots.

Miller is hoping to throw all of the challenged ballots out, and he filed a federal lawsuit last week claiming that write-in ballots must spell a candidate’s name exactly as it appears on the declaration of candidacy.

Even if every challenged ballots is thrown out, Murkowski would still lead by more than 2,000 votes, with only about one-third that number left to count from overseas ballots. A statement on Murkowski’s campaign website Tuesday night said the Senator “will not declare victory until all the overseas ballots are counted.”

Miller spokesman Randy DeSoto indicated in a statement earlier Tuesday that the campaign would push on, even if Murkowski pulled ahead with unchallenged ballots. “Additionally, there are hundreds of ballots yet be counted including those from overseas military personnel, which may draw the overall numbers between the Miller and Murkowski even closer,” he said. “The race is far from over.”

Murkowski was on Capitol Hill this week, but the Associated Press reported she will be returning to Alaska on Wednesday. “Throughout the past several days, Joe Miller has said that he will not continue to contest the election if the votes don’t add up,” campaign manager Kevin Sweeney said in a statement Tuesday. “By the end of the day tomorrow after every Alaskan vote will have been counted, we expect Mr. Miller to keep his word.”

If Murkowski is certified as the winner, she will become the first person since 1954 to be elected to the Senate through a write-in campaign.