A needleless connector has a body having an internal cavity with a sealing ridge, a port, an output flow channel, and a fluid flow path between the port and output flow channel. The connector also has a collapsible valve disposed within the cavity. The valve includes a cylindrical wall having a center axis, an internal surface, and a shoulder configured to sealingly contact the ridge of the body, thereby blocking the fluid flow path. The valve also includes a head fixedly attached to the wall. The head has a smiley cut at a first angular position about the center axis and a continuous top surface that is generally perpendicular to the axis. The valve also includes a first dimple formed in the internal surface of the cylindrical wall. The dimple extends around the internal surface over an angle in the range of 90-270°.