Containers with closures are disclosed. A closure may include at least a polymer orifice reducer configured to be permanently secured to a rim of an opening of a container and a flexible tamper evident seal disposed on the topside of the orifice reducer. The flexible tamper evident seal, optionally foil, covers one or more openings in the orifice reducer. Processes for permanently securing a closure to a container, optionally by forming a heat seal between the orifice reducer and container rim, are also disclosed.