A spiral-wound cross-flow filter element comprising: a permeate tube; and a pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320) attached to the permeate tube, the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320) comprising a plurality of leaves (36; 55; 75; 82, 84; 92; 120) circumferentially spaced around the permeate tube and spiral-wound around the permeate tube in a uniform direction; wherein each leaf (36; 55; 75; 82, 84; 92; 120) comprises: an inlet edge (31; 84; 104); an outlet edge (33; 86; 106), wherein the length of the inlet edge (31; 84; 104) is greater than the length of the outlet edge (33; 86; 106); a tapered distal edge (39; 99; 109) extending between the inlet edge (31; 84; 104) and the outlet edge (33; 86; 106); and a proximal end (37; 107) located adjacent to the permeate tube and comprising two folded proximal edges (47; 67; 87) extending between an inlet end of the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320) and an outlet end (23; 216) of the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320); wherein the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320) is attached to the permeate tube at the inlet end and the outlet end (23; 216) of the folded proximal edges (47; 67; 87) between each leaf (36; 55; 75; 82, 84; 92; 120), wherein each leaf (36; 55; 75; 82, 84; 92; 120) comprises: a bond along the entire length of the inlet edge (31; 84; 104); a bond along the entire length of an outlet edge (33; 86; 106); and a bond along the entire length of the tapered distal edge (39; 99; 109); wherein the bonds seal together adjacent plies of the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320) and provide each leaf (36; 55; 75; 82, 84; 92; 120) with a fluid impervious seal at the inlet edge (31; 84; 104), the outlet edge (33; 86; 106), and the tapered distal edge (39; 99; 109). a permeate tube; and a pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320) attached to the permeate tube, the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320) comprising a plurality of leaves (36; 55; 75; 82, 84; 92; 120) circumferentially spaced around the permeate tube and spiral-wound around the permeate tube in a uniform direction; wherein each leaf (36; 55; 75; 82, 84; 92; 120) comprises: an inlet edge (31; 84; 104); an outlet edge (33; 86; 106), wherein the length of the inlet edge (31; 84; 104) is greater than the length of the outlet edge (33; 86; 106); a tapered distal edge (39; 99; 109) extending between the inlet edge (31; 84; 104) and the outlet edge (33; 86; 106); and a proximal end (37; 107) located adjacent to the permeate tube and comprising two folded proximal edges (47; 67; 87) extending between an inlet end of the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320) and an outlet end (23; 216) of the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320); an inlet edge (31; 84; 104); an outlet edge (33; 86; 106), wherein the length of the inlet edge (31; 84; 104) is greater than the length of the outlet edge (33; 86; 106); a tapered distal edge (39; 99; 109) extending between the inlet edge (31; 84; 104) and the outlet edge (33; 86; 106); and a proximal end (37; 107) located adjacent to the permeate tube and comprising two folded proximal edges (47; 67; 87) extending between an inlet end of the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320) and an outlet end (23; 216) of the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320); wherein the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320) is attached to the permeate tube at the inlet end and the outlet end (23; 216) of the folded proximal edges (47; 67; 87) between each leaf (36; 55; 75; 82, 84; 92; 120), wherein each leaf (36; 55; 75; 82, 84; 92; 120) comprises: a bond along the entire length of the inlet edge (31; 84; 104); a bond along the entire length of an outlet edge (33; 86; 106); and a bond along the entire length of the tapered distal edge (39; 99; 109); a bond along the entire length of the inlet edge (31; 84; 104); a bond along the entire length of an outlet edge (33; 86; 106); and a bond along the entire length of the tapered distal edge (39; 99; 109); wherein the bonds seal together adjacent plies of the pleated filtration membrane (16; 40; 60; 80; 90; 110; 220; 320) and provide each leaf (36; 55; 75; 82, 84; 92; 120) with a fluid impervious seal at the inlet edge (31; 84; 104), the outlet edge (33; 86; 106), and the tapered distal edge (39; 99; 109).