A woven basket can become a sort of accidental kitchen scrapbook when remnants of things kept in it -- seeds, crumbs, old flower petals -- get trapped in the weave. Linen-lined baskets, used in Europe to hold rising bread dough, offer a lovely, practical solution. Many stores carry them, but it's easy to make your own.
To measure a round basket, run a cloth tailor's tape down into it from lip to lip. (For a rectangular basket, repeat for crosswise measurement.) Adding 2 inches all around for a hem, cut a piece of unbleached linen to size. Center the linen in the basket. With heavy linen thread and a sturdy needle, sew the lining in place along the bottom inside edge of the basket using 1/2-inch stitches. (If the basket is tightly woven, use pliers to pull the needle through.) Smooth cloth, and pleat it to fit, making four evenly spaced folds (at corners for a rectangle); secure each fold with one big stitch the depth of the basket. Stitch linen around the basket's outside lip, turning the hem under as you go