The conundrum under discussion was the same one that has confronted the South African firm since its foundation by the buccaneering Cecil Rhodes in 1871: to keep its tight grip on the world diamond market it not only has to control supply but manipulate demand as well.
In the 1930s the problem was especially acute: world depression threatened a collapse in diamond prices that would undermine the Oppenheimer empire. That meeting led to a subtle and prolonged fashioning of public perception, summed up in the immortal 1948 slogan, "A diamond is forever".
By 1984, when the old man gave up the De Beers' chair, US demand had topped $2bn, from $23m in 1939. In the 15 years before his retirement, another campaign had changed Japanese courtship rituals: from a standing start, more than 60 per cent of brides marked marriage with diamonds, not just the ancient Shinto ritual of drinking rice wine from a wooden bowl.
By then the immediate problem, but not the imperatives, had changed. To make sure prices kept rising, De Beers had to fashion ever newer tastes to stop a flood of freshly discovered Russian diamonds breaking the market. It was that torrent that led to the "eternity ring", made up of hundreds of tiny Siberian diamonds sold to an entirely new market of married women, first in the US, then across the world.
As author Edward Jay Epstein put it in his 1982 history, The Diamond Invention: "Again, sentiments were born out of necessity: American wives received a snake-like ring of miniature diamonds because of the needs of a South African corporation to accommodate the Soviet Union."
At midnight tonight, De Beers' troublesome 28-year dalliance with the Russians was due to close, leaving the cartel's control on a knife edge. A $5bn five-year deal formally expires tonight, whereby the Russians let De Beers market 95 per cent of their rough diamond production - a quarter of the world's output by value. Only a last-minute pause, at a tense meeting in Moscow 10 days ago, led to a fragile one-month extension while both sides prepare for further talks in mid-January.
The stakes are high. Earlier this month De Beers' Central Selling Organisation (CSO), which controls 80 per cent of the world market, announced that sales to the trade had reached a record $4.5bn in 1995 and that recent price rises for larger stones had stuck. Production quotas for cartel members, including Russia and Australia's giant Argyle mine, will remain at 85 per cent, however, and the trade is worried that the collapse of the Russian deal would not only flood the market but trigger a domino effect among other producers; diamond prices may not be forever.
De Beers has been here before. The Russian problem had been around ever since Harry Oppenheimer succeeded his father, Ernest - the man who forged the cartel - in 1957.
In the meantime, the South Africans have seen off threats from man-made diamonds, recurrent US anti-trust investigations, anti-apartheid isolation, Israeli attempts to corner the market, and huge smuggling operations in the 1990s out of war-torn Angola.
The answer with the Russians was the same as with other recalcitrants: via a mix of threats, De Beers' buying power, and realisation of self- interest, they were co-opted. Ultimately it is in no one's interest that prices sink and what is in effect polished carbon glass goes the way of coral or pearls.
"Single-channel marketing has ensured long-term stability. The Russians understand that, and that we will always be a dominant influence on the market," a De Beers spokesman said.
Since May 1994, De Beers has been seeking a solution to the desire of Russia to have its cake and eat it: it has guaranteed prices, yet at the same time floods the market with up to $1bn a year of illicit diamonds from its huge strategic stockpile to garner much-needed hard currency.
Talks have also been hampered by political differences between Moscow and the breakaway republic of Yakutia, partners in the main producer Alamazy Rossii-Sakha. Komdragnet, the Moscow-based controller of the stockpile, has also presented a huge obstacle, while recent Russian elections have led to dragging of feet.
Analysts believe a new deal will be struck - possibly a looser arrangement with De Beers as a preferred customer, but backed by binding undertakings on illicit leaking. There was also talk last week of a new diamond exchange, with De Beers helping to sell polished gemstones from Russia's nascent cutting industry.
De Beers also loaned $1bn to Russia in 1990, which was finally paid off in November. It is keeping tight-lipped about a repeat, or any other details, until talks are concluded.
Whenever that comes, self-interest means the price of the diamond on your finger is unlikely to collapse - but the latest crisis will not be the last.
Canada is the latest diamond frontier set to open, with mining giants BHP and RTZ in the hunt with De Beers.
If supply explodes, the cartel's marketing gurus will be tasked again under a new generation of Oppenheimers. Beware, then, the seemingly irresistible urge, fostered by subtle advertising, to rush out for maternity rings or glittering funeral masks.