A package comprising: a first panel (204, 304, 404); a second panel (206, 306, 406), wherein the first and second panels (204, 206, 304, 306, 404, 406) are sealed to each other to form a pouch (200, 300, 400), wherein the pouch (200, 300, 400) includes a main section (314, 414) and a channel section (316, 416); and a product (202, 302, 402) disposed within the pouch (200, 300, 400), wherein the product (202, 302, 402) is capable of flowing from the main section (314, 414) through the channel section (316, 416) to a tip (212, 312, 412) of the pouch (200, 300, 400); wherein the pouch (200, 300, 400) includes a valve (224, 234, 244, 254, 274, 324, 424) that has a curve extending transversely across the channel section (316, 416), wherein the curve is configured such that, when the product (202, 302, 402) flows through the curve, the product (202, 302, 402) flows by a convex side of the first panel (204, 304, 404) in the curve and a concave side of the second panel (206, 306, 406) in the curve; characterized in that: a portion of the first panel (204, 304, 404) that includes the curve is less rigid than a portion of the second panel (206, 306, 406) that includes the curve; wherein the portion of the second panel (206, 306, 406) that includes the curve has a valve deflection constant defined as: C VD = Et D where C VD is the valve deflection constant, E is a modulus of elasticity of the portion of the second panel (206, 306, 406), t is a thickness of the portion of the second panel (206, 306, 406), and D is a diameter of the concave side of the second panel (206, 306, 406) in the curve when the pouch (200, 300, 400) is in a resting state; and the valve deflection constant is in a range from about 46.5 MPa to about 92.4 MPa. a first panel (204, 304, 404); a second panel (206, 306, 406), wherein the first and second panels (204, 206, 304, 306, 404, 406) are sealed to each other to form a pouch (200, 300, 400), wherein the pouch (200, 300, 400) includes a main section (314, 414) and a channel section (316, 416); and a product (202, 302, 402) disposed within the pouch (200, 300, 400), wherein the product (202, 302, 402) is capable of flowing from the main section (314, 414) through the channel section (316, 416) to a tip (212, 312, 412) of the pouch (200, 300, 400); wherein the pouch (200, 300, 400) includes a valve (224, 234, 244, 254, 274, 324, 424) that has a curve extending transversely across the channel section (316, 416), wherein the curve is configured such that, when the product (202, 302, 402) flows through the curve, the product (202, 302, 402) flows by a convex side of the first panel (204, 304, 404) in the curve and a concave side of the second panel (206, 306, 406) in the curve; characterized in that: a portion of the first panel (204, 304, 404) that includes the curve is less rigid than a portion of the second panel (206, 306, 406) that includes the curve; wherein the portion of the second panel (206, 306, 406) that includes the curve has a valve deflection constant defined as: C VD = Et D where C VD is the valve deflection constant, E is a modulus of elasticity of the portion of the second panel (206, 306, 406), t is a thickness of the portion of the second panel (206, 306, 406), and D is a diameter of the concave side of the second panel (206, 306, 406) in the curve when the pouch (200, 300, 400) is in a resting state; and the valve deflection constant is in a range from about 46.5 MPa to about 92.4 MPa.