The sack of potatoes on a crate was hardly noticeable on a recent afternoon at Broadway Fremont Gas.

Sami Abed, owner of the north Minneapolis store, had bought them from Cub Foods down the street for $1 cheaper than he was selling them. Like other convenience store owners, he has to purchase in small quantities so that the produce does not spoil.

Abed was selling it at the urging of the city of Minneapolis, which invested in his store along with nearly 40 other corner stores as part of an ambitious effort to spread fresh fruits and vegetables to small businesses in poor neighborhoods.

This year, after seeing mixed results in its Healthy Corner Store Program, the city is scaling the program back to just 10 stores.

The program started in 2009 out of concern that residents of poor neighborhoods had little access to large grocery stores with fresh food. But Minneapolis is discovering that improving diets in disadvantaged areas requires more than just putting healthier food on convenience stores shelves.

Candy and pop are always a sure bet with customers, according to Abed, but nutritious food can be a gamble.

The cost of convenience Minneapolis is pouring resources into replenishing “food deserts,” or areas where healthy food — especially produce — is scarce. But as the city scales back a program that helps corner stores offer a higher-quality selection, some researchers say that fresher food in stores isn’t enough.

“Pop and snacks and all that, it’s easier to do than produce,” Abed said.

City health workers and nonprofits have encouraged corner stores not only to sell more produce, but also to display it more prominently and be part of community outreach.

But the city realized that it needed to have more intense, long-term relationships with store owners to convince them that stocking healthy foods could actually make money. Without those, according to one city official, the effort was not sustainable: Staff would return a few weeks later and find produce wilted, bruised and forgotten.

“It’s really not enough to just put in a basket of apples and oranges at the front register and call it done and say, ‘Great, the city was here,’ ” said Nora Hoeft, a public health specialist for Minneapolis. “We really need to work more intensively with store owners.”

As city intervention continued, several stores in the program closed, and others struggled to maintain the quality and appearance of produce displays. Health specialists also calculated that stores on average were selling less than $10 a week of produce.

The Star Tribune found that like Abed’s store, many corner stores that have been targeted by the city are near large chains offering cheap produce, such as Cub Foods, Aldi, Rainbow Foods, Supervalu and Target. Half of the 10 stores that will be in the next round of the program are a half-mile or less from such chains.

That trend poses a challenge to the program’s success, as owners of corner stores frequently buy produce from bigger grocery chains, rather than more cheaply from wholesalers, because they purchase in small quantities to ensure it will not go bad.

Corner store owners have also said they usually do not make money on fruits and vegetables, but like the idea of working with the city and finding new ways to draw in customers. The city has spent $29,000 on the effort, largely with the help of state funding.

“We’re going to try even if we don’t make money on vegetables and fruits,” Abed said. “Cub Foods is not far away from here and Aldi’s is just up the road. … If we sell it for $4, they sell it for two-something.”

The program grew out of an ordinance passed in 2008 requiring stores to carry at least five types of perishable produce, among other things. But a city review of north Minneapolis stores the following year found that three-quarters did not meet the standard.

And some researchers have found tenuous connections between how we eat and the types of food that are the most available to us on grocery store shelves.

One study in 2011 tracked low-income people in Minneapolis, Birmingham, Ala., Oakland, Calif., and Chicago, and found little connection between fruit and vegetable consumption and access to supermarkets, though proximity to fast food led them to eat more of those foods.

A study published this month in Health Affairs that examined the opening of a new supermarket in a Philadelphia “food desert” also found that it did not lead to greater consumption of produce, and that other interventions might be needed to aid residents in those areas.

In Minneapolis, offerings at participating corner stores vary widely. Toni’s Market in south Minneapolis has a variety of produce that could compete with any grocery store, and likewise, Minnesota Halal Market, which largely caters to Somali immigrants, has expansive bins of fruits and vegetables. Conversely at the North Side’s Brix Market, some green peppers on display had gone bad and the produce shelf in the back was difficult to find.

The latest phase of the program includes about five stores already working with Minneapolis and five new ones, though others that have worked with the city in recent years, such as Abed’s Broadway Fremont Gas, will continue offering produce, but will have less city supervision.

Among the new stores targeted is Midwest Halal Market at the corner of Portland and Franklin avenues, which already sells an impressive array of fresh cilantro, ginger, chili peppers, tomatoes and other produce. Such items do not turn much of a profit, according to manager Mohamed Abdi, but they draw in customers — even if they complain about the high price.

Sami Abed, owner of Broadway Fremont Gas in north Minneapolis, says soda and snacks are easier to sell than produce.

“We cannot compare to Cub Foods and Rainbow when we are a corner store,” he said.

But what truly pays the bills? Junk food of all kinds, from pop to doughnuts, along with cans of beans that have a long shelf life.

“We make more money on this,” Abdi said.