A check valve includes a tubular sleeve bounding a longitudinally-extending flow-through passage for fluids, a disc having a first material affixed along a first portion of its periphery to a flexible hinge member, and a bill affixed at a first end to one or more of the sleeve, the flexible hinge member, and the disc. The check valve also includes one or more of the following of (i), (ii), and (iii): (i) at least one groove, rib, insert, or combination thereof that extends longitudinally along a length of the disc, the bill, or both the disc and the bill; (ii) at least one groove, notch, rib, insert, or combination thereof that extends laterally along a width of the bill; and (iii) at least one ripple that extends longitudinally along a length of the bill and, optionally, longitudinally along a length of the disc.