These days, at the age of 75, Mr Dobrynin is in virtual retirement, a consultant to the Russian Foreign Ministry in Moscow. But for 26 years, a period spanning almost two-thirds of the Cold War, he was the Soviet ambassador in Washington, with personal access to six presidents. The "back channel" that ran through Mr Dobrynin helped the superpowers defuse crises even as the obligatory public rhetoric seemed to make them worse. And he made policy too, with proposals he would cable back to Moscow with the proviso "unless instructed otherwise". He rarely was.
Now he has produced his memoirs. Not only are they by far the most authoritative account yet of the Cold War from the Soviet side and of the machinery of Soviet foreign policy-making, In Confidence is also a manual of diplomacy, brimming with good stories.
Famously, a diplomat is an honest man sent abroad to lie for his country. Mr Dobrynin did his share of that - above all, unwittingly, during the Cuban missile crisis when he was lied to by his bosses in the Kremlin. But a diplomat also lives by trading honest information. People, he notes, "do not ask you back if you just ask questions and do not tell them anything in return". Not so Mr Dobrynin.
He tells of a lame-duck Lyndon Johnson, so obsessed with the notion of a valedictory summit in Moscow that he failed to grasp the importance of the Soviet invasion of Czechoslovakia. In 1968, Richard Nixon was so feared by Moscow as a reckless anti-Soviet crusader that the Kremlin instructed Mr Dobrynin to offer Hubert Humphrey aid, including money, in his election campaign. Mr Dobrynin indirectly broached the issue, praying that Humphrey would get the drift. Mercifully he did, and declined. "The matter was thus settled to our mutual relief, never to be discussed again."
Later Nixon developed so warm a relationship with Leonid Brezhnev that as Watergate reached endgame, an American president's closest political friend was his opposite number in Moscow. Mr Dobrynin tells how a jet- lagged Brezhnev drank too much his first evening at Nixon's Western White House in California during the 1973 summit and spilt the beans to the President about his Politburo colleagues. "Anatoly, did I talk too much?" an alarmed General Secretary asked the next morning. "Yes," answered Dobrynin, "but I was careful not to translate everything."
Mr Dobrynin was, of course, an apparatchik. He may blame Moscow rather than Washington for almost every crisis of the period, but contrary to the belief of a captivated Ronald Reagan among many others, he was a loyal Communist, with little time for dissidents, whom he considered irritants to smooth US-Soviet relations.
On internal Soviet affairs, Mr Dobrynin comes off the rails towards the end. He believes the system could have been reformed to preserve a unitary Soviet Union "that ranked high among the democracies of the world". Its failure was due to the blunderings of Mikhail Gorbachev, urged on by the "evil mastermind" Alexander Yakovlev and lured by Western flattery into giving away the shop. It is perhaps as well Mr Dobrynin is retired. But on the subject he knows best, he is matchless.
"The highest form of diplomacy," he writes, "does not consist of trying to drown differences in champagne and vodka toasts at feelgood summit meetings, nor of papering over unresolvable issues with communiques written in gobbledygook, but in finding ways to disagree without doing profound damage to an important strategic relationship." The Cold War is over - but not the need for the skills he enumerates.