Joseph I. Lieberman was clocked in his Democratic primary fight against Ned Lamont this month but has vowed to fight on, as an Independent, to retain one of Connecticut’s two seats in the Senate. He may win, and if he does, he says he’ll then declare himself a Democrat and go on as if nothing happened.

But something did happen, and Mr. Lieberman is kidding himself if he thinks it didn’t. Though a Democratic primary in a northeastern state in the middle of a sizzling summer doesn’t exactly bring out the mainstream of the party, rules are rules. If he was happy enough to claim the Democratic nomination in the three times he won those primaries, he ought to accept the verdict in this month’s contest.

Which doesn’t mean he should necessarily stand down.

It might mean that he ought to run as an Independent – and then actually serve as an Independent.

There currently is an Independent in the Senate, James M. Jeffords of Vermont. He’s a Republican apostate, but in most ways he is a Democrat, getting his committee assignments from the Democrats and organizing his life and work among the Democrats. That’s the model all 15 Independents elected since 1900 have taken, though for a few weeks in 1953, Wayne Morse of Oregon, a one-time Republican, did place a folding chair in the middle of the aisle between the two parties. He eventually sided with the Democrats.

But there’s another way to think about being an Independent, and though it has never been done in the modern age, it has some appeal at a time when the public has little but contempt for both parties. In this model, an Independent would truly be independent.

There are lots of reasons why the independent road is a difficult road. Though not mentioned in the Constitution, the parties are entrenched in the Capitol, and they control committee assignments, the flow of legislation to the floor, the rhythms of political life in both chambers, and even such prosaic items as the location of a lawmaker’s office. The organized political parties provide the organizing principles of the Congress.

That’s the reality. It also is an indictment.

An independent-minded lawmaker with a national constituency of his own, a reputation for probity, fairness and integrity, and the ability to attract media attention might be able to survive the scorn of the two parties and even do what every legislator dreams of accomplishing but seldom approaches: make a difference in the shape of the institution in which he serves and in the national debate.

Mr. Jeffords isn’t the only prominent New Englander to have served as an Independent in recent years, and the other two actually took the label to heart, as governors far from Washington. They were Lowell P. Weicker Jr. of Connecticut (a former Republican senator) and Angus King of Maine. And even if they served as executives, not as legislators, their status apart from the political fray in fact allowed them to remain above the fray. As a result, Gov. King is remembered as one of the most successful governors of his generation, and Gov. Weicker was able to win passage of a state income tax.

“There was a big advantage for me,” says Mr. Weicker, who was defeated by Mr. Lieberman in a bitter 1988 campaign and who now is a strong supporter of Mr. Lamont. “I had to pull together a coalition of Republicans and Democrats who knew the only way for the state to get out of its economic mess was having an income tax, and neither party could afford to be blamed for that.”

The road for Mr. Lieberman would be harder, which may be all the more reason to take it.

Almost all of the leading Democrats who cheered him when he was on the party’s national ticket six years ago – including his colleague, Christopher J. Dodd of Connecticut; the first lady at the time, Sen. Hillary Rodham Clinton of New York; and scores of others – already have abandoned him like a car broken down on the side of the highway. These may not be the kind of friends he wants.

But contemplate a world outside one of the two parties: No leaders telling you what to do. No leaders telling you what to think. No leaders telling you how to vote. You don’t have to check with anyone before you decide what is right or wrong. You don’t have to worry about any interest group. You don’t have to worry about offending anyone.

In this role, Sen. Lieberman would have no institutional authority. But he might have moral authority.

“The parties remind me of one of those guys in the gangster movies when someone says: He’s already dead, he just doesn’t know it yet,” says Mr. King, who served as Maine’s governor from 1995 to 2003. “There’s great running room for someone who is trying to call ’em as he sees ’em and to do the right thing. The parties are too ideological, too rigid, too closed and too attentive to their base, leaving the center with nowhere to go.”

Hardly anyone thinks the political system is working as it should. Mr. Lieberman was a trailblazer when he became the first member of his faith to win a place on a national ticket. He could be a trailblazer in the Senate as well, restoring faith in politics – and having far more power as a single true Independent in the Senate than he ever could have had as vice president in the White House.