Crude oil prices hit their highest level in three months overnight in response to growing signs that Saudi Arabia is winning its war on U.S. shale producers.

A raft of data in recent days has suggested that the period of heavy oversupply in the global crude market is coming to an end, as shale producers run out of cash for drilling, and low prices encourage higher demand around the world.

Futures prices for West Texas Intermediate, the U.S. benchmark blend, topped $49.50 a barrel for the first time since July in overnight trading although they have retreated a little ahead of a closely-watched release on U.S. oil stocks later Wednesday. The global benchmark Brent, meanwhile, topped $53/barrel for the first time since the end of August. Both are now up some 8% from their levels of a week ago.

A number of factors have gone into the sudden price move. Russia’s escalation of the war in Syria has injected a classic ‘geopolitical risk premium’ into prices over the last week, and there have also been suggestions that Saudi Arabia and Russia, the world’s two biggest oil producers, may start to coordinate supply–although such talk comes with the heavy caveats that Russia has never voluntarily restrained output and the two countries are bitterly divided over Syria (Russian jets have been pounding Saudi- and U.S.-backed rebels in the last week, rather than the jihadists of Islamic State).

But it’s the hard data and accompanying forecasts that have been chiefly responsible. Baker Hughes’ closely-watched rig count showed that the number of drilling rigs in the U.S. turned down sharply in September after signs of a brief revival in the previous two months. At 848, the number of U.S. drilling rigs is only half what it was in January, and the lowest level since 2003. The Department of Energy said Tuesday it estimated U.S. oil production fell by 120,000 barrels a day last month, and will continue to fall through mid-2016. It now expects U.S. crude output to fall to an average of 8.9 million b/d next year from 9.2 million this year.

But rising demand is also helping to rebalance the market. The International Energy Agency now expects global demand to rise by 1.7 million b/d this year. Reuters quoted Patrick Pouyanné, the chief executive of French major Total SA TOT , as telling a conference Tuesday that the increase could be even bigger.