The marketing agreement between the White Wave unit of US dairy company Dean Foods and US coffee retailer Starbucks is proceeding better than expected, according to company executives.

Under the deal, announced in February, White Wave became the sole provider of soymilk to Starbucks, supplying the product to 4,000 Starbucks outlets in North America, reported Dow Jones News Service.

“We’re actually already running ahead of forecast,” Steve Demos, White Wave founder and president, was quoted by Dow Jones as saying.

Rob Grady, director of venture development for Starbucks, said White Wave’s soymilk would be in 95% of Starbucks’ North America outlets by next week.

Grady added that the companies had had to focus on ensuring that they can meet demand if it continues to grow as quickly. Soymilk is “one of the top two fastest growing beverages at Starbucks right now,” he said.