We can all imagine the legion of politicians, media executives and entertainment moguls who are not getting a lot of sleep these days, wondering when their turn in the sexual harassment spotlight will come. That’s a good thing – hopefully, that fear is reforming behavior for them and their peers. An important question is, however, how do we instill the same fear in the hearts of men whose misdeeds won’t land them on the front pages or in the midst of a Twitter storm because they don’t have a public profile.

What we’ve learned from the current flurry of revelations about sexual harassment is that public shaming may reform behavior but the law, as is, won’t. That means we need a broad agenda to change the law to protect the millions of women who don’t work for a famous boss.

In so doing, we should be especially careful to protect low-wage women workers, who often have less economic mobility than better educated, higher-wage workers, and are even less able to quit when they end up in a hostile work environment.

One obvious first step is to extend coverage of the law to smaller workplaces and give victims more time to decide to bring a claim. Beyond this, there must be a greater cost to employers for engaging in sexual harassment or allowing it to go on.

In high-profile cases, companies are finally taking action because the cost to their bottom lines of bad publicity is so high. How can we change the law to get employers outside of the limelight to worry about their bottom lines if they don’t do the right thing? We should impose higher monetary penalties, create sanctions for blacklisting workers who step up, and make sure that company owners and higher-level corporate officials have skin in the game by expanding the universe of who can be held responsible for harassment.

When sexual assault takes place at work, it should be criminally prosecuted just as if it had occurred elsewhere

Strong anti-retaliation protections also should be enacted to prevent employer reprisals and put the power of the law and enforcement agencies behind workers who, on their own, can’t push back when their employers try to push them out for speaking up.

And when retribution comes soon after a worker reports violations – as it often does – the law should presume that retaliation has occurred unless the employer can prove otherwise, and should also include damages to fully compensate wronged employees.

When cases are settled, the facts are often hidden because of non-disclosure clauses, which prevent the victims from speaking out. Disallowing such clauses would help prevent patterns from continuing without detection. And requiring settlements to be approved by courts or anti-discrimination agencies – just as courts or the labor department must approve federal minimum wage settlements – would prevent workers from being bullied into settling on the cheap.

It would also create a public record of settlements, giving workers access to important information and enabling the government to intervene when a clear pattern has emerged.

Because so many workers are often too intimidated to come forward, new approaches to enforcement should accompany new laws. Enforcement agencies should embrace a strategic vision, in which they target likely violators, proactively investigate workplaces instead of reactively waiting for complaints, and focus intently on deterring violations and creating a culture of compliance.

And when sexual assault takes place in the workplace, it should be criminally prosecuted just as if it had occurred anywhere else. Low-wage workers in particular need this protection, since they toil in industries with high levels of sexual assault, and not just harassment – restaurants, farms, hotels.

Finally, and perhaps most importantly, stronger worker organizations would go far in creating a new, more democratic workplace culture in our country, enabling workers to raise their voices against all kinds of labor abuses. Unions and other workers’ groups provide the strength in numbers that help people speak out.

Innovations that enable workers to have a collective voice on the job would go a long way toward stopping not only the Harvey Weinsteins, but also the outrageous and inappropriate boss next door.

The women who have unleashed the post-Harvey Weinstein fury should be incredibly proud of their courage in demanding the public’s attention. But we can’t let this moment pass without using it to do the quieter work of fixing this problem for all women.