Facebook and Twitter's chief executives are being cross-examined by US senators for the second time in three weeks.
The two were summoned to answer questions about how their platforms had limited distribution of a controversial article about Joe Biden's son published ahead of the US election.
But they are also being challenged over their handling of posts by President Trump and others who have contested the vote's result.
The tech firms face new regulations.
In particular, President-elect Biden has suggested that protections they currently enjoy under a law known as Section 230 should be "revoked".
It says the platforms are generally not responsible for illegal or offensive things users post on them.
Mr Biden has said this allows them to spread "falsehoods they know to be false".
Republicans have also voiced concern about the law. They claim it lets social media companies take decisions about what to leave up and take down without being transparent about why, making bias possible.
"When you have companies that have the power of governments, have more power than traditional media outlets, something has to give," said the Republican Senator Lindsey Graham, who is chairman of the Senate Judiciary Committee.
Facebook's Mark Zuckerberg and Twitter's Jack Dorsey both addressed the issue in their opening remarks.
Mr Dorsey urged the politicians to work with Twitter to avoid changes that might cause "the proliferation of frivolous lawsuits, and severe limitations on our collective responsibility to address harmful content".
Mr Zuckerberg added that any update must preserve "the freedom for people to express themselves and for entrepreneurs to build new things".
The two tech CEOs also defended their record in handling the 2020 election.
But Mr Dorsey acknowledged that Twitter's decision to block links to the New York Post article about Hunter Biden had been "wrong", and that its failure to subsequently restore the newspaper's own tweets about the story had required a further policy change.
"I hope this... demonstrates our ability to take feedback, admit mistakes and make all changes transparently to the public," he said
Mr Zuckerberg avoided direct reference to the matter.
However, he used the opportunity to challenge recent claims by Democrats that Facebook had been slow in removing posts that promoted insurrection and violence.
"We strengthened our enforcement against militias and conspiracy networks like QAnon to prevent them from using our network to organise violence or civil unrest," Mr Zuckerberg said.
The two tech leaders have been challenged over some of their recent decisions.
The Democratic Senator Richard Blumenthal wanted to know why Facebook had not banned Steve Bannon.
President Trump's former top advisor recently called for the beheadings of disease expert Dr Anthony Fauci and the FBI director Christopher Wray in a video he posted to both Twitter and Facebook.
Twitter threw him off its service, but Facebook only froze Mr Bannon's page.
Mr Zuckerberg said Mr Bannon "did violate our policies" but had not clocked up enough strikes to permanently lose access.
And when the senator called for a rethink, Mr Zuckerberg responded: "That's not what our policies would suggest we should do."
Mr Zuckerberg went on to dispute reports that Facebook had forgiven infractions by both of Donald Trump's sons and the news site Breitbart, among others, in order to avoid accusations of bias from conservatives.
"Those reports mischaracterise the actions that we've taken," he said.
The Democratic Senator Dianne Feinstein followed up with questions to both executives over their responses to President Trump's posts about election fraud, which lacked factual basis.
She asked Twitter's chief whether he thought adding labels but allowing the tweets to remain visible went far enough.
Mr Dorsey responded that he believed providing "context" and "connecting people to the larger conversation" was the right path to follow.
Senator Feinstein went on to ask Mr Zuckerberg if he felt enough had been done to prevent people delegitimising the election's result given that hashtags for Steal The Vote and Voter Fraud had garnered more than 300,000 interactions on its platforms in the hours after Mr Trump falsely declared victory.
"I believe we have taken some very significant steps in this area," Mr Zuckerberg responded, pointing to information it had placed at the top of the screens of US-based Facebook and Instagram users.
"I think that we really went quite far in terms of helping to distribute reliable and accurate information about the results."
Voter fraud warnings
The Republican Senator Ted Cruz took a different tack, asking why Twitter was "putting purported warnings on virtually any statement about voter fraud".
When Mr Dorsey repeated his earlier point about linking people to conversations, Mr Cruz pushed back.
"No you're not. You're putting up a page that says 'voter fraud of any kind is exceedingly rare in the United States'. That's not linking to a broader conversation. That's taking a disputed policy position."
Mr Cruz added that Twitter only had the right to take such a position if it accepted it was a publisher, which would mean losing the right to Section 230's protections.
And he challenged both firms to disclose how many times they had blocked Republican and Democratic candidates for office in the 2016, 2018 and 2020 elections to reveal any discrepancy.
Neither tech chief would give a firm commitment to do so.
Meanwhile, the Republican Senator Michael Lee brought up Twitter's suspension of an account belonging to Mark Morgan, the commissioner of US Customs and Border Protection.
The action was taken after Mr Morgan tweeted that the wall on the border with Mexico had helped stop "gang members, murderers, sexual predators and drugs from entering our country".
"What exactly is hateful about [that]?" asked Senator Lee.
Mr Dorsey acknowledged that the action had been taken in error.
"There was a mistake and it was due to the fact that we had heightened awareness around government accounts," he explained.
The Senator responded: "I understand that mistakes happen, but what we're going to see today is that mistakes happen... almost entirely on one side of the political aisle rather than the other."