The Republican Party has the opportunity to name at least two women to high-ranking national security posts in the next Congress and the incoming Trump administration, history-making moves that could help the GOP mend fences after a bruising campaign season that alienated many female voters.

Sen. Kelly Ayotte of New Hampshire, who narrowly lost her bid for a second term, is in the mix for Defense secretary, while Rep. Kay Granger of Texas is campaigning to take the gavel of the House Defense Appropriations Subcommittee. Both positions have, until now, only been held by men.

The two women, both hawks who have advocated increased defense spending, are considered long shots for the jobs. But some defense observers see a political and strategic benefit in promoting Ayotte and Granger to these prominent posts.

The Republican Party, long dominated by white men, no doubt has a perception problem only exacerbated during an election in which the party’s standard bearer — and now president-elect — was roundly criticized as a misogynist as he campaigned against Hillary Clinton, the first female presidential nominee from a major party.

As Republicans fill out their leadership rosters for the 115th Congress, the party’s faces on Capitol Hill will continue to be predominately white men. The same goes for Donald Trump’s expected Cabinet, where the front-runners for top posts so far are mostly white men who are contemporaries of the 70-year-old president-elect.

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Mackenzie Eaglen, a national security analyst at the American Enterprise Institute, acknowledged that putting women in these senior national security positions isn’t a silver bullet for the Republican Party or national security policy and spending. Nonetheless, she said, it can’t hurt.

Ayotte and Granger could help diversify the faces of the party. They would bring a different perspective and may also be more willing to cut deals than their male counterparts, a characteristic that would undoubtedly come in handy in the next Congress and administration.

“I do think there’s a desire among women, generally speaking, to compromise more often,” Eaglen said. “There has been a lot of gridlock and there really have only been men at the table.”

Ayotte’s ascendancy to Pentagon chief would also check a lot of other boxes for the new administration. She is a strong ally of Senate Armed Services Chairman John McCain of Arizona, who is already agitating to serve as a check on the incoming commander in chief, sharply warning Trump last week against creating a cozy relationship with Russia.

Ayotte, who is a vocal member of the Armed Services Committee, is an unabashed hawk who has gone to the mat with the Obama administration on issues such as the Guantanamo Bay detention facility and cost-saving efforts to retire the Air Force’s venerable fleet of A-10 Warthog close air support aircraft. A former New Hampshire attorney general, she also would bring legal expertise to a job that increasingly requires it, Eaglen said.

For the party as a whole, moving Ayotte to the Pentagon would allow the GOP to keep one of its rising stars in the spotlight.

“She would be fantastic,” Eaglen said, echoing sentiments aired by other security hawks.

But Ayotte finds herself at a distinct disadvantage as the Trump transition team appears intent on picking longtime loyalists for key administration posts. During her re-election battle, she distanced herself from Trump, refusing to attend the Republican convention or campaign with the nominee.

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In the House, Granger is up against House Appropriations Chairman Harold Rogers of Kentucky, who has his eyes on the defense job now that he is coming to the end of his term as full committee chairman.

If history is any guide, the decision for defense appropriations chairman will ultimately be up to Rodney Frelinghuysen of New Jersey, who will be taking on Rogers’ job in the next Congress. The House Republican Steering Committee does not typically intervene much in the cardinal-selection process.

“It’s the chairman’s decision,” a GOP lobbyist said. “I could see if they were leapfrogging somebody. But there’s a school of thought that the big chairman should get whatever he wants because he’s done a good job.”

Still, the lobbyist noted, it is a difficult decision for Frelinghuysen because Granger has put in her time on the subcommittee. Frelinghuysen was the No. 2 Republican on the defense panel for years, so he is acutely aware of Granger’s desire to take the gavel, the lobbyist added.

Another lobbyist source tracking the competition for defense appropriations chairman gives Granger, the outgoing chairwoman of the State-Foreign Ops Appropriations Subcommittee, a decent chance of claiming the defense gavel, thanks to her long tenure on the subcommittee. Republicans, the lobbyist said, may also be swayed by the opportunity to put a woman in a high-profile national security post.

“She is qualified and capable and ready to do it,” Eaglen said.