A closure (20, 20A) for a container that has an opening to the container interior wherein contents may be stored, said closure (20, 20A) comprising: a body (30, 30A) that is either (a) a separate structure for being attached to said container at said opening, or (b) a structure formed as a unitary portion of said container at said opening, and wherein said closure body (30, 30A) has a deck defining (i) a pour aperture that can communicate with said container opening and that can accommodate pouring out of the contents through said pour aperture, and (ii) at least one vent aperture that can communicate with said container opening and that can accommodate the in-venting of ambient atmosphere through said at least one vent aperture into said container, and said closure body (30, 30A) has a pour spout projecting outwardly from said deck and extending at least partway around said pour aperture; and a lid (32, 32A) for accommodating movement relative to said closure body (30, 30A) between (a) a closed position sealing against said closure body (30, 30A) to prevent flow of the contents outwardly of said closure body (30, 30A), and (b) an open position permitting flow of the contents outwardly of said closure body (30, 30A); and wherein said pour aperture is elongate with its length oriented along a central axis line that bisects said closure body and said pour aperture; said pour aperture has an arcuate narrow end; said pour aperture has a wide end (52") that (i) is wider than said narrow end, and (ii) is located closer to said at least one vent aperture than is said narrow end; said at least one vent aperture has a maximum width as measured along a line perpendicular to said closure body central axis line, and said maximum width of said at least one vent aperture is greater than the width of at least a portion of said pour aperture as said pour aperture width is measured along a line perpendicular to said closure body central axis line; wherein said closure (20, 20A) is characterized in that said length of said pour aperture is at least three time greater than the maximum width of said pour aperture as the pour aperture maximum width is measured along a line perpendicular to said closure body central axis line, and in that said at least one vent aperture is circular and is spaced away from the nearest portion of said pour aperture by an amount that is less than the diameter of said at least one vent aperture. a body (30, 30A) that is either (a) a separate structure for being attached to said container at said opening, or (b) a structure formed as a unitary portion of said container at said opening, and wherein said closure body (30, 30A) has a deck defining (i) a pour aperture that can communicate with said container opening and that can accommodate pouring out of the contents through said pour aperture, and (ii) at least one vent aperture that can communicate with said container opening and that can accommodate the in-venting of ambient atmosphere through said at least one vent aperture into said container, and said closure body (30, 30A) has a pour spout projecting outwardly from said deck and extending at least partway around said pour aperture; and a lid (32, 32A) for accommodating movement relative to said closure body (30, 30A) between (a) a closed position sealing against said closure body (30, 30A) to prevent flow of the contents outwardly of said closure body (30, 30A), and (b) an open position permitting flow of the contents outwardly of said closure body (30, 30A); and (i) is wider than said narrow end, and (ii) is located closer to said at least one vent aperture than is said narrow end;