A valve system for use in a subterranean well, the valve having multiple closure devices, or a closure device and a device for protecting the closure device. A valve system includes a valve with a closure assembly. The closure assembly has a closure device and a protective device which alters fluid flow through a flow passage of the valve prior to closure of the closure device to thereby protect the closure device. A safety valve system includes a safety valve with a closure assembly having at least two closure devices arranged in series for controlling flow through a flow passage of the safety valve. Another safety valve system includes a safety valve assembly including multiple safety valves arranged in parallel. One portion of fluid from a fluid source flows through one of the safety valves, while another portion of fluid from the fluid source flows through another safety valve.