Senators in both parties are touting their move last week to require sexual harassment training for all members and aides.

What they don’t mention is that many Senate offices already required training or were moving toward it — and that their vote did nothing to reform a system for handling complaints that critics say deters victims from coming forward.

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Now, some lawmakers are fighting to ensure that the Senate’s unanimous approval of mandatory training doesn’t make further reforms harder by offering political cover to members who would prefer to move on. Bipartisan talks on an overhaul of the Capitol’s harassment policy, which critics in and out of Congress say is stacked against victims, remain in their early stages.

“It’s a really important conversation that the country is having” about harassment, said Sen. Kirsten Gillibrand (D-N.Y.), who’s waged underdog battles for GOP support to beef up sexual assault protections in the military and on campus.

“But I also believe it’s the tip of the iceberg,” she said in an interview. “There’s not a clear recognition about how pervasive this is in society.”

Gillibrand and a handful of other senators are vowing to make the harassment training requirement — which the House has yet to approve — the first step toward rooting out workplace misconduct in Congress. And they’re well aware that the issue is sensitive for an institution that reflexively protects its own.

Current rules require victims to submit to mediation and counseling before filing a complaint, a process that can stretch on for months while they remain at work with the alleged perpetrator of harassing behavior. Gillibrand is working on her own proposal set for release this week, with Rep. Jackie Speier (D-Calif.) taking the lead in the House, to streamline what harassment victims say is a stressful and difficult system for handling complaints on the Hill.

She’s not alone. Aides working on the issue said Sen. Chuck Grassley (R-Iowa), a chief author of the 1995 law that first required Congress to follow federal workplace standards, has taken a personal interest in a stronger harassment policy. An aide said Grassley is also examining broader changes to the system for handling harassment complaints.

And Minnesota Sen. Amy Klobuchar, who shepherded the mandatory harassment training plan to its quick passage last week, is keeping the issue going through her post as top Democrat on the Rules Committee.

“The Senate should continue to examine how harassment claims are handled to ensure we support victims in our effort to make clear that harassment of any kind is not and will not be tolerated in the Senate,” Klobuchar said in a statement to POLITICO. “This was simply a first step.”

Klobuchar has formed a bipartisan working group of committee members to help shape a broader proposal that would make filing a claim and going through dispute resolution easier for harassment victims, a Democratic aide said.

The sexual assault allegations that have rocked Roy Moore’s Senate bid appear to have helped speed the measure requiring training for aides and senators through the upper chamber. And now some aides privately hope that the Alabama scandal can keep lending momentum to shift the Hill’s harassment policy.

The House will begin its own debate on updated workplace misconduct rules at an Administration Committee hearing on Tuesday, with Speier set to testify alongside Rep. Bradley Byrne (R-Ala.), a former employment attorney.

Speier plans to use her testimony to describe mandatory training as the “easiest step” for lawmakers to take and “to reiterate that reform to the complaint process is what is really going to change things,” according to a spokeswoman. A longtime advocate for stronger harassment standards on the Hill, Speier recently shared her own story of getting forcibly kissed by a superior during her years as a congressional aide as the social media-driven movement known as #metoo began raising awareness of the issue.

Gillibrand and Speier’s bill would make sweeping changes to the rules that the Hill’s Office of Compliance currently uses to handle harassment complaints. The legislation would remove the requirement that victims go through mediation before filing a complaint and create a confidential adviser within the compliance office to help victims through the process.

The Democratic women’s proposal also is expected to require public disclosure of congressional offices that are the subject of complaints and have negotiated a settlement from the fund that the compliance office uses to compensate victims, according to Speier’s office. In addition, the bill is set to remove the requirement that harassment victims sign a nondisclosure agreement in order to start mediation or receive a settlement from the compliance office’s fund, which is paid for by taxpayers.

From fiscal 2012 through February of this year, the compliance office’s fund paid out $2.9 million to settle 69 Hill harassment cases, according to internal documents obtained by POLITICO. However, those settlements cover multiple types of workplace misconduct settlements, and specific data covering the cost of resolving sexual harassment complaints are not publicly available.

While the allegations against Moore and accused harassers in Hollywood and the media keep a national spotlight on the issue, Gillibrand, Klobuchar and Speier are optimistic about being able to seize the moment to push through further changes. No Republican co-sponsor has yet emerged for a broader harassment bill, but Speier’s office said she is reaching out to Reps. Ryan Costello (R-Pa.) and Bruce Poliquin (R-Maine), early backers of her proposal to require harassment training in the House.

“Sexual harassment goes far beyond the cases you read in the headlines,” Klobuchar said. “It’s a widespread problem that affects too many men and women in too many places, professions and industries — including the United States Congress, where we have an obligation to set an example of conduct and policies to the country.”

Gillibrand agreed that “we have a lot of work left to do.”

“No one reform is going to change everything,” she said, “but we have to at least keep trying.”