Downhole valve having incrementally adjustable open positions and a quick close feature

A valve that is usable with a well includes an indexer and a closing mechanism. The indexer includes a profile to establish a sequence of open settings for the valve, and the indexer is adapted to respond to first control stimuli to transition the valve through the settings according to the sequence. The closing mechanism is adapted to operate independently of the sequence in response to a second control stimulus to close the valve.