What will probably stay their hand, at least for a while longer, are the continuing high levels of crude oil inventories. Until there is a substantial drawdown on these inventories, any rise in output would be suicidal for the oil price, the producers and their economies.
For those who consume oil rather than produce it - which is most of the world - a low oil price is, of course, no bad thing. The three-day week which followed the oil shock of 1973, and the mini recession which followed the Gulf War show just how destructive high oil prices can be.
By contrast, a low oil price helps subdue inflation, stimulates growth and keeps down the cost of motoring. And although the short-term impact on the oil companies may be painful, it teaches them to find more efficient ways of extracting the stuff and running their businesses. Without the becalmed oil price of the last 12 months, it is debatable whether the world would have seen quite the same level of opportunistic mergers within the oil industry.
On the other side of the ledger, low oil prices wreak havoc with the economies of the producing countries, and when those producers are also emerging economies such as Russia, that can spell trouble. Six months ago, when the oil price was languishing at under $10 a barrel, no-one would have dared guess it could rise to today's levels. There again, commodity prices are up right across the board. It wouldn't pay to bet on them staying there. The recovery is a fragile one, and if the US goes into a tailspin, they'll go straight back down again.