A method of variably restricting flow in a subterranean well can include resisting the flow through a sidewall of a tubular string, and then selectively opening a device in response to a predetermined pressure signal being transmitted. The opening of the device can substantially reduce a resistance to the flow through the tubular string sidewall. A flow restrictor system for use with a subterranean well can include a flow restrictor which resists flow through system, a pressure sensor, and an initially closed device which opens and thereby permits the flow to bypass the flow restrictor, in response to a predetermined pressure signal being detected by the sensor.