No Republican woman has ever served on the Senate Judiciary Committee in its 200-year history — a fact that became an embarrassing national story for Republicans during the Brett Kavanaugh confirmation hearings this summer.

Senate Majority Leader Mitch McConnell thinks it’s time to diversify, but he’s got a short list of possible candidates.

There are five Republican women who are currently incumbents in the Senate, guaranteed to serve next term. They all told Vox that they aren’t interested in switching up their current committee assignments.

All five — Sens. Susan Collins, Lisa Murkowski, Joni Ernst, Shelley Moore Capito, and Deb Fischer — have signaled that they’re already on committees tied to their policy focuses. Capito, for example, joined the Senate Commerce Committee to focus on infrastructure and rural broadband, issues important to the voters she represents in West Virginia.

“I have pretty good committees right now,” Capito told Vox. “I think I’m pretty well suited where I am.”

That leaves McConnell with two possible candidates: Marsha Blackburn, a lawmaker who stood out in the House for her conservative values and just won statewide in Tennessee, and, potentially, Cindy Hyde-Smith, a sitting senator who faces a runoff election in November for a Mississippi seat. Blackburn and Hyde-Smith’s offices did not immediately respond to requests for comment.

The gender disparity on the Judiciary Committee became major news this summer when Republicans decided it was better to hire a female prosecutor to question Christine Blasey Ford about her allegation that Supreme Court nominee Kavanaugh sexually assaulted her in the 1980s (a claim he denies) than question her themselves. If they had, they risked facing blowback over images of an all-white-men panel pressing an alleged sexual assault victim just weeks before an election.

Things didn’t get much better when Sen. Chuck Grassley suggested there were no women on the committee because they weren’t willing to do the work. “It’s a lot of work — maybe they don’t want to do it,” he initially said, ultimately walking these comments back.

McConnell has acknowledged the stark gender disparity on the committee between parties, while noting that it’s been challenging to find a woman for the Judiciary Committee in previous years. It’s a reality rooted in a systemic problem: A big reason McConnell has struggled to convince a woman to join the panel is that there are so few women representing the Republican Party in the first place.

There could be, at most, seven Republican women in the Senate — pending the outcome of Mississippi’s race

As things currently stand, Republicans simply don’t have that many women they can ask. There are just seven Republican women in next year’s Senate (assuming Hyde-Smith makes it through her runoff election later this month).

On the Democratic side, conversely, there are more than double that (still a disproportionately low number), with 17 women set to serve in the 116th Congress. And while Republicans have yet to add a woman to the Judiciary panel, Sens. Dianne Feinstein and Carol Moseley Braun became the first Democratic women to sit on the committee after they were elected in 1992. Currently, the committee has four Democratic women.

As McConnell indicated, he’s had a tough time when it came to adding gender diversity to the committee in the past. Having such a small pool of women in the Senate is likely a major factor.

Republicans really want Marsha Blackburn to say she’ll do it

Blackburn — the newly elected lawmaker from Tennessee — is seen as a major contender for the seat, according to a Politico report. Blackburn is an eight-term Congress member who had previously represented Tennessee’s Seventh Congressional District.

She’s a conservative firebrand, and her policy background could make her a good fit for the Judiciary Committee: She’s previously spearheaded a wide range of tech and telecom legislation, which could fall into the panel’s purview, for example. While in the House, she chaired the Energy and Commerce Committee’s telecom panel — a subcommittee that had jurisdiction over issues including data privacy and intellectual property.

Blackburn hasn’t indicated whether or not she’d be interested in the Judiciary position just yet. “I don’t know where you’re hearing that,” she told Politico when asked about the possibility.

If she does end up taking on the role, she’ll be taking a major step in helping the Republican Party address its yawning gender gap on the pivotal Senate panel, which has far-reaching jurisdiction over everything from Supreme Court nominees to immigration policy.

Her election has already helped bolster the number of Republican women in the Senate — something the party needs to continue working on, if it wants to improve representation in committees and the chamber across the board. Changes to the Judiciary Committee could be next.