Brands such as Black Box, Bota Box and the Wine Cube by—get ready—Target use California grapes, and are stored with bags that collapse to keep out oxygen so the wines last longer—some up to six weeks. They’re still cheap: a three-liter carton (that’s four bottles) goes for about $20.

That’s still unlikely to attract connoisseurs. “My patrons would laugh me right out of the restaurant if I brought a box over to their table,” says James Endicott, a Manhattan sommelier. But the wines should be a hit for less discerning drinkers. “Wine should taste good. It’s that simple,” says Steph Waller, a California wine lover who is working on a book called “Box of Wine: A Cultural Icon.” Waking up without a headache can’t hurt, either.