A medical valve has a housing with an inlet housing and an outlet housing. The interior of the inlet housing and/ or the outlet housing has a contact surface. A resilient element sits within the housing and is configured to control fluid flow through the inlet. The resilient element has a proximal portion with a normally closed aperture configured to open when actuated by a medical device. The resilient element also has a distal portion adjacent to the outlet, and a central portion between the proximal portion and the distal portion. The central portion has a wall that defines a fluid chamber in the open mode and in the closed mode. The wall has at least one projection extending radially outward. The projection is configured to maintain compressive contact with the contact surface of the housing and to apply an inwardly compressive force on the resilient element, increasing the wall stiffness.