Walk in to the corner store at Cedar Avenue and E. 26th Street to grab a bag of chips or a soda, and customers first run into an obstacle.

Just inside the entrance to Cedar Food & Grill, there’s a large display packed with an ever-growing variety of fresh foods: peaches, oranges, avocados, tomatoes — even whole coconuts and bunches of cilantro. Further back, coolers filled with eggs and milk are so popular that store employees have to restock them several times each day.

Six years after Minneapolis became the first city in the United States to require small shops to stock healthy foods, stores like Cedar Food & Grill are prime examples of how a new policy and some guidance can lead to big changes. Now, city officials are looking to double down on their efforts.

The Minneapolis City Council will soon consider a proposal that would tighten standards for small food retailers, increasing the amount of fresh produce, protein items, milk, juice and whole-grain breads they must keep in stock. In addition, the plan could require some dollar stores to get a grocery license and follow the new rules.

The idea behind the initial staple foods ordinance was to bring healthful options to neighborhoods without nearby grocery stores to help combat rising problems with obesity and other diseases. But Council Member Cam Gordon, who introduced the revised law, said the city’s current rules don’t go far enough.

“The food requirements are pretty minimal,” he said. “When we passed them a few years ago, they didn’t seem so minimal.”

Gordon’s proposal is modeled in part on the standards of the government Special Supplemental Nutrition Program for Women, Infants, and Children, known as WIC. Among the plan’s specifics, which will be considered at an Oct. 20 public hearing:

• Stores would have to stock 30 pounds or 50 items of at least seven varieties of fresh fruits and vegetables, up from the current requirement of five varieties with no minimum amount.

• Offerings would need to include at least 3 varieties of meat, poultry, fish or vegetable proteins, at least 6 containers of a dozen eggs, at least 192 ounces of canned beans and four packages of dried beans and lentils, up from a basic requirement of three types of protein items, two of them fresh.

Melissa Laska, a University of Minnesota public health professor who studies the impact of increasing access to healthy foods, said customers changed their habits after similar upgrades.

She studied the impact of those changes and found a major increase in the number of customers buying reduced-fat milk instead of whole milk, a threefold increase in purchases of whole grain products and a drop in the purchase of white bread. Among WIC participants in New York, obesity rates dropped about 6 percent for babies and nearly 3 percent for young children.

Laska said it appeared stores were able to overcome such challenges as finding space and equipment for proper refrigeration or building customer demand for new items.

“We did the evaluation a year post-policy change and the stores seemed in that time to have been able to overcome the hurdles they were facing,” she said.

In Minneapolis, those hurdles have been significant for some businesses. A year after the staple foods ordinance was passed, worried that many stores weren’t meeting the new requirements, the city launched a Healthy Corner Store Program. The effort, funded by grant money, provided guidance to store owners about how to display and market fresh foods and put them in touch with suppliers.

The program evolved over the years, starting with a small group of stores, then expanding, and again shrinking after stores dropped out or failed to improve without intensive assistance.

Some stores struggled to comply. The city has issued warning or violation notices to nearly 60 stores and gas stations.

The city’s log of problems — found on annual licensing visits — shows many stores failed to have enough fruits and vegetables in stock. Some had only one type on display and a few had let the produce go bad.

Stores found to be out of compliance are issued a warning. If inspectors find the same problems again within two years, businesses are fined $200. Records show seven fines issued since 2008.

Now, the Healthy Corner Stores Program is working with 10 businesses. Kristen Klingler, a senior public-health specialist with the city’s health department, said officials are ready to support more stringent foods rules.

“We’ve certainly planned for supporting additional stores in the future, perhaps not in the same way,” she said. “We’ve worked really intensively with stores in the past, and with limited resources we can’t work with every store in Minneapolis. But we are willing to offer a variety of training and education to help them.”

Gordon acknowledges that tighter standards can pose a challenge, but said the city’s assistance program should provide some relief.

Mohamed Wadi, owner of Cedar Food & Grill, sells enough produce that he can keep prices relatively low. On a recent afternoon, the best deal was two apples for 99 cents. But for businesses that buy their fresh foods from nearby supermarkets, competitive pricing is a challenge.

While Wadi has had success turning a profit on his healthful offerings, he’s not sure all stores will be able to get the same results if the requirements are tightened.

“It’s going to be a big loss for (smaller stores),” he said. “But for the stores with traffic, it will be good.”

At Fremont Market, near North 36th Street and Fremont Avenue, cashier Ray Azem said he’s seen evidence customers tastes are changing — and they may even be willing to pay a little more for better produce. His store now works with distributor of local fruits and vegetables, rather than buying them from a local supermarket.

A display in the store last week offered bags of potatoes ($2.99), watermelon ($5.99), apples and oranges (69 cents), along with about a dozen other options.

Azem said he knows for sure of at least one person who has gotten in the habit of eating more healthfully since Fremont Market began selling fresh food.

“I never ate fruit and veggies before,” he said.