Concerns are rising as enrollment falls in the St. Paul Public Schools, fueling the likelihood of tough conversations ahead in the boardroom and at the negotiating table.

School board members on Tuesday received an annual report on the district’s school-choice lottery that showed 1,177 students were unable to get into some of the district’s most popular schools in 2017-18.

That kind of demand might seem like a good thing. But that’s not always the case in St. Paul, which soon will welcome a new superintendent, Joe Gothard. The district announced Tuesday that it has a verbal agreement with him for a three-year contract paying $232,000 in the first year.

Families shut out of their top choices for district schools, especially at the elementary level, often will send their kids to competing charter schools or other districts, rather than another school in the St. Paul system. With those students goes the revenue they generate, and as enrollment tumbles, budget pressures mount. St. Paul faces a $27.3 million shortfall for 2017-18.

The district and its teachers are preparing for another round of contract talks, and board Chairman Jon Schumacher took the unusual step recently of advocating in a districtwide e-mail that teachers back away from limits on classroom sizes that were heralded as a major victory by the union during 2013-14 contract negotiations.

Smaller classes mean fewer seats available at popular schools not only to kids in each of the district’s seven attendance zones, but also to low-income students in other neighborhoods looking to take advantage of an integration program called Reflecting St. Paul. Under that program, the district sets aside 25 percent of available seats at low-poverty schools for students from poorer and more diverse areas.

In his e-mail, Schumacher said that the hard enrollment caps have increased costs by $11 million to $13 million annually, and that greater flexibility is needed so the district can fund science, art, music and other electives valued by many families.

“Every day we compete with a variety of educational institutions that offer our families choices,” he said. “We cannot continue to put our district at a competitive disadvantage, so we need to talk about ways to make class-size decisions work better and smarter.”

Convincing the St. Paul Federation of Teachers to modify its stance will be a challenge.

Asked about Schumacher’s message, and the potential of raising the caps, Denise Rodriguez, the union’s president, said a week ago: “No, we are not open to that.”

Last week, the union launched its campaign for a new two-year contract by distributing a booklet, “The Schools St. Paul Children Deserve: Progress Report,” which says it aims to “hold firm to current class-size commitments in all grades and subjects.” The federation argues that smaller class sizes lead to better individualized instruction and stronger relationships with students.