To impeach or not to impeach? That may be the wrong question.

Yes or no: Do you favor impeaching President Donald Trump? That’s the question Democratic politicians around the country are being battered with – at town halls, in fundraisers, during TV interviews. Support for impeachment has been slowly rising among Democrats in Congress, within the large Democratic presidential field, and among the American people.

Now that retired special counsel Robert Mueller has spoken publicly about his Trump-Russia investigation, effectively leaving next steps to Congress, the question has gained fresh urgency.

But “impeachment, up or down” may not be the right question. Indeed, in responding to a president who defies subpoenas and whom a significant portion of Americans view as unfit for office, Congress is not facing a binary choice. The options are many, including another form of sanction for perceived wrongdoing: censure, a formal reprimand in the form of a majority resolution by one or both houses of Congress.

“It’s a symbolic gesture that would please no one, but it might be the best alternative,” says a Democratic strategist, speaking on background.

Unlike impeachment, which is the constitutional procedure for expelling a president before the end of his term, censure is not mentioned in the U.S. Constitution. But it’s an option – rarely used – that would at least convey moral outrage over certain presidential actions, for those who feel it. The Mueller report found no provable conspiracy between Trump associates and Russia in the 2016 election, but it detailed 10 examples of potential obstruction of justice by the president.

Democratic pollster Mark Penn, a critic of the Mueller investigation, agrees that “censure makes sense” – in part because holding such a vote against the president in the Democratic-controlled House would put “a lot of Republicans in a bind.” Mr. Trump enjoys 90 percent support among Republican voters, which makes it politically dangerous for GOP members to vote against him. So far, the only Republican in either chamber to come out in favor of impeachment is the libertarian-leaning Rep. Justin Amash of Michigan.

A House censure vote against Mr. Trump could hold some political peril for Democrats. As with impeachment, Mr. Trump could wear a censure resolution as a badge of honor. And the party’s liberal base would likely perceive it as a mere slap on the wrist in the face of what many Democrats see as egregious or even illegal presidential behavior. But would it lead them to stay home in the 2020 election? Mr. Penn is doubtful.

“It’s pretty unlikely activists will pass on an opportunity to vote against Trump,” the pollster says.

For now, though, debate among Democrats centers squarely on impeachment – or more precisely, whether to launch a formal impeachment inquiry. The hope is that such an inquiry would unearth further evidence of presidential wrongdoing, either in matters related to the Mueller investigation or elsewhere, including Mr. Trump’s financial dealings.

In effect, a preliminary impeachment inquiry is already starting, though not in name. The warm-up act comes Monday, when former Nixon White House counsel John Dean testifies before the House Judiciary Committee on obstruction of justice, along with former U.S. attorneys and other legal experts. Mr. Dean was the star witness against President Richard Nixon in the 1973 Watergate hearings that eventually led to the 37th president’s resignation.

House Judiciary Chairman Jerrold Nadler has announced additional hearings in coming weeks that will focus on “other important aspects of the Mueller report.”

On another track, the full House is scheduled to vote Tuesday on whether to hold Attorney General William Barr and former Trump White House counsel Don McGahn in contempt for failing to deliver subpoenaed documents and, in Mr. McGahn’s case, for defying a subpoena to testify. The contempt resolution is expected to contain language that boosts Democrats’ efforts to obtain Trump tax returns.

So far, no key witnesses in the Trump-Russia inquiry, including Mr. Mueller himself, have agreed to testify in Congress. In a rare public statement last week, Mr. Mueller said “the report is my testimony.” But Democrats still want him to appear before Congress, if only to give voice to key points from his report, based on the assumption that few Americans will read the 448-page tome. Democrats have yet to subpoena Mr. Mueller.

Meanwhile, the list of House Democrats supporting an impeachment inquiry is growing – now at 59 (out of 235), according to a New York Times count. Among the two dozen Democrats running for president, 11 now support an inquiry. Overall public support for impeachment is also growing, though still not a majority. Mr. Penn’s latest Harvard-Harris poll shows support for impeachment and removal from office at 37 percent, up from 28 percent in April; support for “no action” is at 42 percent, and 20 percent favor censure. Among polled Democrats, 60 percent favor impeachment; among independents, it’s 36 percent.

Time is not on the pro-impeachment side, barring an explosive revelation. With each passing day, the November 2020 election takes up more oxygen and boosts the argument that the voters should decide Mr. Trump’s fate. Democrats are keenly aware that, based on what’s known, the Republican-controlled Senate would not come close to convicting and removing the president even if he were impeached by the House.

So the calendar, in effect, is House Speaker Nancy Pelosi’s friend, as she tries to fend off pro-impeachment forces within her caucus. Speaker Pelosi maintains impeachment is still on the table, but only in the event of a major new revelation.

Here the argument becomes circular: The likeliest path to explosive new information, if it exists, would come via a formal impeachment inquiry, congressional Democrats say. They believe it would boost their case in court as they seek access to grand jury testimony and documents underlying the Mueller report. But most House Democrats fear a formal House move toward impeachment could boost Mr. Trump politically, as it did President Bill Clinton in 1998.

“Right now, if the House impeached Trump, the Senate wouldn’t convict. That inoculates him,” says Rick Tyler, an anti-Trump Republican commentator. “He’ll say he was exonerated. He’ll say it was all a witch hunt.”

Centrist House Democrats are also advising caution.

“I think people now are just all about the contempt vote next week,” a leading House moderate told reporters on background Tuesday. “Hopefully that will let off enough steam to avoid the impeachment vote. I think people still think – like me – oversight, oversight, oversight, you know? And use the courts.”

Whether there’s potential for a modern-day John Dean to step forward is another question. Historian Ken Hughes has his doubts.

Mr. Dean had agreed to become a key witness in exchange for a lighter sentence, stemming from his involvement in the Watergate scandal. But “it’s not clear now that the Democrats in the House have that kind of leverage over any current members of the Trump administration,” says Mr. Hughes, a research specialist and expert on Watergate at the University of Virginia’s Miller Center.

With former administration officials, there are major disincentives to cooperating with Congress. Some may be motivated by continuing loyalty to the president. There are also professional reasons to avoid testifying, Mr. Hughes says.

“Former Trump administration officials can fear being ostracized and fear losing job opportunities,” he says. “They can fear losing access to their former colleagues in the administration, which makes them less useful as lobbyists.”

Staff writer Jessica Mendoza contributed to this report.