A program created by a group that organizes farmworkers has persuaded companies like Walmart and McDonald’s to buy their tomatoes from growers who follow strict labor standards. But high-profile holdouts have threatened to halt the effort’s progress.

Now the group, a nonprofit called the Coalition of Immokalee Workers, is raising pressure on one of the most prominent holdouts — Wendy’s — which it sees as an obstacle to expansion.

The Immokalee workers’ initiative, called the Fair Food Program, currently benefits about 35,000 laborers, primarily in Florida. Over the last decade, it has helped transform the state’s tomato industry from one in which wage theft and violence were rampant to an industry with the some of the highest labor standards in American agriculture.

Under the Fair Food Program, buyers like Walmart and McDonald’s agree to pay 1 to 4 cents more per pound of tomatoes. The growers, in turn, agree to pay farmworkers at least the local minimum wage, to which the premium adds a bonus, and to meet a set of labor standards like providing shade and water for workers and ensuring freedom from physical and sexual abuse. Some of the practices are required by law but flouted on many farms.