A gas bubble is circulated from a well by a system that maintains the well and bottom hole pressure substantially constant by progressively increasing the casing pressure as needed to maintain the drill pipe pressure substantially constant. An incrementally increasing casing pressure reference signal is produced by detecting each occurrence of the drill pipe pressure falling a predetermined amount below a drill pipe pressure reference signal. The casing pressure reference signal is compared with the actual casing pressure. A throttling valve is closed a corresponding amount if the acutal casing pressure is less than the casing pressure reference signal. The throttling valve is opened a corresponding amount if the actual casing pressure is greater than the casing pressure reference signal.