A combination of an overcap and a fitment for a container, which together in an initially assembled orientation prevent, but can be subsequently operated to permit, communication through the fitment, said combination comprising: said fitment having a spout defining an access passage, an interior sealing surface, and an exterior sealing surface (45A, 45B); said spout has an outer end defining a rim around said access passage; and said overcap having a top deck from which extends an elongate, hollow plug, said elongate, hollow plug having a plug sealing surface for engaging said fitment interior sealing surface to create a first seal (47A, 58A) when said overcap and said fitment are in said initially assembled orientation, a skirt extending over at least a portion of said spout and having a skirt sealing surface (63A, 63B) for engaging said fitment exterior sealing surface (45A, 45B) to create a second seal (45A, 45B/63A, 63B) when said overcap and said fitment are in said initially assembled orientation, and an annular channel defined between said elongate, hollow plug and said skirt into which said fitment spout extends to accommodate relative rotation between said overcap and said fitment; and said combination of the overcap and the fitment being characterized in that said fitment further comprises a base that can be sealed to a flexible pouch and that has a base outer end from which said spout projects; said first seal (47A, 58A) is axially spaced a first distance from said base outer end; said rim is axially spaced a second distance from said base outer end; said first distance is less than half of said second distance. said fitment having a spout defining an access passage, an interior sealing surface, and an exterior sealing surface (45A, 45B); said spout has an outer end defining a rim around said access passage; and an access passage, an interior sealing surface, and an exterior sealing surface (45A, 45B); said spout has an outer end defining a rim around said access passage; and said overcap having a top deck from which extends an elongate, hollow plug, said elongate, hollow plug having a plug sealing surface for engaging said fitment interior sealing surface to create a first seal (47A, 58A) when said overcap and said fitment are in said initially assembled orientation, a skirt extending over at least a portion of said spout and having a skirt sealing surface (63A, 63B) for engaging said fitment exterior sealing surface (45A, 45B) to create a second seal (45A, 45B/63A, 63B) when said overcap and said fitment are in said initially assembled orientation, and an annular channel defined between said elongate, hollow plug and said skirt into which said fitment spout extends to accommodate relative rotation between said overcap and said fitment; and said combination of the overcap and the fitment being characterized in that a top deck from which extends an elongate, hollow plug, said elongate, hollow plug having a plug sealing surface for engaging said fitment interior sealing surface to create a first seal (47A, 58A) when said overcap and said fitment are in said initially assembled orientation, a skirt extending over at least a portion of said spout and having a skirt sealing surface (63A, 63B) for engaging said fitment exterior sealing surface (45A, 45B) to create a second seal (45A, 45B/63A, 63B) when said overcap and said fitment are in said initially assembled orientation, and an annular channel defined between said elongate, hollow plug and said skirt into which said fitment spout extends to accommodate relative rotation between said overcap and said fitment; and said combination of the overcap and the fitment being characterized in that said fitment further comprises a base that can be sealed to a flexible pouch and that has a base outer end from which said spout projects; said first seal (47A, 58A) is axially spaced a first distance from said base outer end; said rim is axially spaced a second distance from said base outer end; said first distance is less than half of said second distance.