Just days after Republican Joe Miller allowed rival Lisa Murkowski to be seated in the U.S. Senate, the Alaskan announced that he will not pursue further challenges to her election.

Friday’s announcement concludes a battle between Miller and Murkowski that began in late summer, when he shocked establishment Republicans by defeating Murkowski in Alaska’s Republican primary for the Senate. Murkowski, one of several incumbents to lose in a primary in 2010, absorbed the surprising loss and mounted a rare write-in campaign to pursue a rematch with Miller in the general election.

Despite long odds and an even longer last name, Murkowski, a member of one of Alaska’s most famous political families, won the write-in vote. But Miller questioned the results and pursued a series of legal challenges, arguing that many misspellings of her name were improperly counted.

Miller’s legal challenges of Murkowski’s November election, in which she recorded more than 10,000 more votes than Miller, were rejected by an Alaska Superior Court, the Alaska Supreme Court and a U.S. District Court in Anchorage. Earlier in the week, Miller said he wouldn’t try to block the certification of Murkowski’s election so that Alaska would have a proper Representative in the Senate, but he continued to talk about taking his dispute higher in the court system.