(FORTUNE Magazine) – The phone call came when Egypt's 1967 war with Israel had just broken out. Aristotle Onassis would lease his entire merchant fleet -- if he had an answer within an hour. ''I was cutting the grass on a Saturday,'' recalls Sir Peter Walters, 56, BP's chairman since 1981 but a mere vice president at the time. ''I couldn't get anybody more senior, so I just decided to do it.'' Tanker prices had already tripled since the war began, but by the following Monday they had doubled again. Says Walters: ''I suppose if it had gone the other way, I wouldn't be here today.'' Instead he went on to tackle even tougher choices with the same calm decisiveness. To stanch losses in BP's refining operations, Walters cut capacity by 40% -- more than any other major oil company. He also launched what London oil analyst David Gray describes as a ''serious clean-out'' of the senior executive suites. The only son of a police inspector who died when Sir Peter was 14, he came to BP after earning an economics degree at Birmingham University. Relaxed and reflective, he sees himself as ''very much a strategist'' who lets day-to-day operations ''tend to themselves.'' Walters and his wife, Patricia, who have three children, live in North London about 20 minutes from BP's headquarters. Last spring Walters made his priciest decision yet -- paying $7.5 billion for the 45% of Standard Oil of Ohio that BP did not already own. Says he: ''It's better to invest in a mature business we know a lot about than be seduced into fast-growing businesses where our chance of emerging as No. 1 or No. 2 is problematical.'' Sounds like another good call.