A liquid-dispensing container includes a housing and a poppet mounted to the housing and movable along an axis between an open position and a closed position. The poppet includes a base portion comprising a relatively rigid material and an elastomeric portion comprising an elastomeric material having a tensile elastic modulus less than the elastic modulus of the rigid material. The elastomeric portion can include an outer section engaged with an outer surface of the base portion and an inner section integrally formed with the outer section and forming a self-closing valve. In one construction, the self-closing valve includes a cylindrical section having a tapered wall thickness. Preferably, the outer section includes a circumferential seal (e.g., a groove) and a circumferential clearance adjacent the circumferential seal. The outer section can further include a retention cleat having a retention surface at an acute angle relative to the axis.
