Rep. Gregg Harper has dropped his bid to become Republican Conference secretary, narrowing the only three-way GOP leadership race to two candidates.

The Mississippi lawmaker sought a spot at the elected leadership table by touting his willingness to take on unenviable tasks for Speaker John Boehner, R-Ohio, especially a post on the Ethics Committee.

The same argument could just as easily be applied to another position for which Harper might be a candidate. His decision to step out of the leadership race is touching off speculation that he will seek the gavel of the House Administration Committee, where he is now the second-ranking Republican and chairman of a subcommittee.

House Administration Chairman Dan Lungren, R-Calif., trails in a close race against Democrat Ami Bera in his Sacramento-area district. At last count, Lungren was down by almost 1,800 votes, but the race has not been called and he has yet to concede.

“Dan Lungren has been an impressive chairman, and I’m hopeful that he will return to Congress,” Harper said in a statement.

The House Administration Committee is one of the few to which all members are appointed by the Speaker. Boehner is sure to hold off on making any decisions until Lungren’s race is resolved.

Harper, who just won his third House term, has been his class’s representative on the influential Republican Steering Committee since being elected. His decision to exit the leadership race almost certainly means he will no longer have a role in that capacity, as neither third-term representatives nor the House Administration Committee chairman is guaranteed a steering committee seat. The conference secretary, on the other hand, is.

Reps. Virginia Foxx of North Carolina and Jeff Denham of California are now left alone to vie for the conference secretary slot.

Foxx is close to Boehner and has long sat on the Rules Committee. She could be helped by a desire among some Republicans to promote women in leadership roles, especially after losing big among that demographic at the polls last week.

Denham is well-liked, has been a prolific fundraiser and has a large base of support in his massive freshman class. But his California district is perennially competitive and being a member of leadership would make him an even more appealing target for Democrats.

Conference secretary is the No. 6 spot on the leadership rung. The incumbent is Rep. John Carter of Texas, who is leaving the leadership.