As politicians in Washington slash budgets and break promises, local governments are forced to pick up the pieces. New York City’s 51-member City Council is critical to this effort, trying as best it can to fill gaps in housing, education, welfare, immigration, the environment and other important matters.

But attending to big-ticket problems is only part of the job. Each council member represents the equivalent of a midsize city — about 160,000 constituents. Calls come in constantly from people who need help fighting a dishonest landlord or muting a neighborhood bar or keeping the local deli from shutting its doors. Council members must also keep a hard eye on the city’s powerful mayor and his $85 billion budget.

Sadly, New Yorkers as a whole do not give the City Council races the attention they deserve. Turnout in city primaries has been lamentably low given the importance of the jobs. In one district with nearly 50,000 registered Democrats, only about 7,000 are expected to show up at the polls to pick their candidate.

We can hope for better on Sept. 12, when Republicans and Democrats will be asked to choose their favorites in the 2017 primaries. Many incumbents have no real challengers, but here are five competitive races that we believe deserve special attention in the Democratic primary. In all five districts, the winning Democrat usually prevails in the general election in November.

The district, and the Council, will lose the talented Daniel Garodnick at the end of this year because of the city’s regrettable term limits law, which New York voters have approved three times and which limits council members to two four-year terms. Fortunately, there are several worthy contenders for the seat. The top three are Keith Powers, a former aide to two respected Albany politicians and an ex-lobbyist from a large city firm; Bessie Schachter, also a veteran Albany aide and a community leader; and Marti Speranza, who ran Women Entrepreneurs NYC (WE NYC), which has helped women establish businesses across the city.

For all the talent in this field, Mr. Powers is the strongest candidate, with an impressive 22-point reform plan. He wants to improve the city’s already excellent campaign finance law, in part by lowering the limit on individual campaign contributions. He would try to make Council voting records easily available online and to restrict lobbying by former city officials. Mr. Powers’s own past as a lobbyist is not disqualifying; he pledges not to have any contacts with his old firm. He promises to also follow the Garodnick system of putting details of every meeting — who, when and why — on his website.

The incumbent, Councilwoman Helen Rosenthal, is facing a rematch with Mel Wymore, a community activist who nearly won the seat four years ago. The Times endorsed Mr. Wymore in 2013, and he has argued well for better constituent services and such improvements as a vacancy fee to limit the time allowed for empty storefronts.

Still, Ms. Rosenthal deserves another four years in office, if only for her courageous support for a new school desegregation plan in the district. She has also pushed to protect tenants being overrun by developers and unscrupulous landlords.

The area’s departing council member, James Vacca, has enthusiastically endorsed Marjorie Velázquez as his replacement. Ms. Velázquez, who started her career in corporate finance, has been a community leader working on transportation issues, keeping housing affordable and helping small businesses.

A former State Senate aide, John Doyle, is also running, but Ms. Velázquez’s main threat is from Mark Gjonaj, a member of the State Assembly. Mr. Gjonaj’s Albany record is modest, and he has too many connections to the old Bronx political machine. By far the most promising choice for this district would be Ms. Velázquez.

This one is easy. Assemblyman Francisco Moya deserves every primary vote in this district. His opponent is former State Senator Hiram Monserrate, who seems to be hoping that voters will not recall the video showing him dragging his girlfriend through an apartment lobby after he had just slashed her face with a piece of glass, that he was thrown out of the State Senate after being convicted of misdemeanor assault, and that he later pleaded guilty to misusing public funds and was sentenced to two years in prison.

Mr. Monserrate, who has shown little remorse, simply does not belong in public service. Mr. Moya, in contrast, has worked in Albany to increase the minimum wage, reform the criminal justice system and provide more protections for construction workers. He would be a credit to this district.

Councilman Carlos Menchaca, a Mexican-American, is fighting to stay on for another four years. He deserves that extra time to continue his work helping immigrants now under siege as they try to stay in the country. He has pushed the city to provide lawyers for tenants facing housing court, and he has held up waterfront developments, arguing that they need to serve the whole community, not just the hip and moneyed crowd. He has important endorsements from many public officials, including two prominent members of Congress, Nydia Velázquez and Jerrold Nadler.