When we think of food deserts, we often picture low-income, urban areas overrun with convenience stores and Taco Bells, but a few retailers around the country are defying this trend.

The prevailing assumption is that residents either don’t know what they’re missing or don’t have the means or motivation to travel for fresh food. But factors beyond socioeconomics can conspire to create food deserts. Insufficient space, heavy traffic flow, high rent costs and other obstacles can make it tough for retailers to turn profits, leaving potential consumers wanting for a spot to shop.

But what if retailers rethought the very parameters of what makes a store?

Realistically, everything from store size to shape to services offered could be open to reimagination, and a few tweaks just might enable retail success in cramped, congested or commuter neighborhoods. For instance, a city block may not be able to house a 40,000-square-foot supermarket, but there could be enough space for a small natural products store. And what if the classic urban standby, the corner store, sold organic frozen burritos instead of Twinkies and Fritos? How about if a shop bucked brick and mortar and was constructed entirely from recycled, sustainable materials?

A few innovative retailers across the nation are, in one way or another, turning the traditional definition of what constitutes a food store on its head. Although their long-term profitability and impact on community health may not be solidified for some time, these pioneers are attempting to show that food deserts can in fact become oases for retail opportunities.