A pleated neckdown bag for lining a receptacle is disclosed wherein the bag is made of a flexible plastic film. The disclosed bag has one or more pleat portions (18) fixed at points around the mouth portion (26) of the bag to reduce the circumference of the mouth portion relative to the circumference of the body portion (14). The reduced circumference mouth portion of the neckdown bag can be fitted over a supporting receptacle. The top portion (12) of the bag is thereby more securely held to the support, and the mouth portion is more securely held in an open state, since the narrowed mouth portion of the bag can better engage a support such as the rim of a waste bin. Bag embodiments having flat and flat rectangular constructions, convenient for manufacture, storage, shipping, and dispensing, are also disclosed. Also disclosed is a tabbed neckdown bag embodiment with a tab (52) modifying means to advantageously modify stress and strain at and near the conjunction of a seam and mouth portion of a neckdown bag. The tab is intended to reduce or eliminate the possibility of tearing of the bag at or near a seam in the neighborhood of the tab. The tab projects from a tab base (58), defined between first (54) and second (56) reentrant arcuate portions of a mouth edge (36), and a top seam portion (20) of the bag extends across the tab base and into the tab. Also disclosed is a tab embodiment, usable in a pleated neckdown bag having a flat construction, where inclusion of the tab does not limit certain advantages pertaining to a flat bag construction.