The four leading candidates for the Democratic presidential nomination are locked in a tight race with less than a month to go before the all-important Iowa caucuses, with a majority of voters still saying their minds are not definitely made up, according to a new survey conducted by the state’s definitive pollster.

The poll found that Sen. Bernie Sanders (I-Vt.) has the support of 20% of likely Iowa Democratic caucus-goers, compared to 17% for Sen. Elizabeth Warren (D-Mass.), 16% for former South Bend, Indiana, Mayor Pete Buttigieg, and 15% for former Vice President Joe Biden.

A close race in Iowa, the first state to vote, could set the tone for a contentious and potentially costly battle for the Democratic nomination to challenge President Donald Trump. A victory for Sanders, Warren or Buttigieg could provide them with the momentum necessary to directly challenge Biden for the nomination. But a strong performance by the former vice president could lock down his substantial lead in national polling.

No other candidate in the race breaks the crucial 15% viability threshold necessary to win delegates to the Democratic National Convention. Sen. Amy Klobuchar (D-Minn.) has the support of 6% of voters, and entrepreneur Andrew Yang has the backing of 5% of the electorate. The results mean Yang is unlikely to qualify for the next Democratic debate, which is set to be held on Tuesday in Iowa.

Legendary Iowa pollster J. Ann Selzer conducted the survey, which was sponsored by CNN and The Des Moines Register.

The poll shows plenty of potential for movement in the race’s final four weeks. Just 40% of voters said their minds are definitely made up on which candidate to support, while 45% said they could be persuaded to back another candidate and 13% haven’t settled on a first choice yet. (At the same point before the 2016 caucus, nearly 60% of voters had made up their minds.)

The last iteration of this poll was conducted in mid-November. Since then, Sanders has improved his position, jumping from 15% to 20%. Buttigieg has fallen after leading the field with 24% of the vote. Neither Warren nor Biden saw significant movement.

The peculiarities of the caucus system — in which voters are required to switch who they are backing if their preferred candidate doesn’t break 15% at their caucus site — means paying attention to voters’ second choices is important: A full third of the electorate says Warren is either their first or second choice, with Sanders and Buttigieg close behind at 32% and 31%, respectively. Twenty-seven percent said Biden is either their first or second choice.

The poll also shows voters are continuing to value a candidate’s ability to defeat Trump more than almost every other quality: 58% said a candidate having a “superior chance of winning in November” was “extremely important,” a trait only topped by a candidate’s “ability to unite the country,” which 69% of voters said was extremely important.

When asked whether it was more important that the winner of the caucus be able to defeat Trump or for the winner to share their stances on the issues, 55% said beating Trump was more important, while 40% said it was important for a candidate to agree with them on the issues. That’s a significant change since November, when 63% said beating Trump was more important and 32% said it was important for a candidate to agree with them on the issues.

The poll of 701 likely Democratic caucus-goers, conducted between Jan. 2 and Jan. 8, has a margin of error of plus or minus 3.7 percentage points.