By Devika Krishna Kumar

May 17 (Reuters) - A rally in U.S. crude oil prices recently has put the market on its firmest footing since the rout started in 2014, with the spread between prices for near-term delivery and future delivery narrowing, suggesting the worst of the supply glut may be over.

Oil prices in global markets have been lifted in the past week by news of falling U.S. production and output disruptions in Canada and Nigeria.

The production cuts are seen helping to rebalance a market awash with excess crude oil, pushing up prices for NYMEX June futures delivery up as much as 11 percent in the last four days. It settled on Monday at $47.72 a barrel.

Traders are watching the relationship between futures contracts expiring later this year and similar contracts expiring in late 2018. The spread, or contango, has narrowed to its smallest margin since November 2014.

The narrowing contango suggests excess supply is finally being reduced after years of overproduction, but if U.S. shale producers ramp up drilling again the market may yet fall back.

With several U.S. shale producers saying they would turn the spigots back on if prices recovered to about $45 a barrel, the market has been bracing itself for renewed supply as prices recovered from 12-year lows, but that may not happen quickly.

"We're not seeing any signs that the U.S. energy industry is in a hurry to respond to a jump in demand because they're still cutting back on projects," said Phil Flynn, senior energy analyst at Price Futures Group.

As prices inched close to $50 a barrel last week, the oil rig count fell further to October 2009 lows, suggesting U.S. shale producers may yet need even higher prices to restart production.

The rebound in near-term prices has also driven hedging activity that has suppressed the prices of later-dated contracts. The discount for crude for delivery in December 2016 versus delivery in December 2018 narrowed to $1.21, after a spread as steep as $8 in December 2015.

The December 2016 discount to December 2017 contract , one of the most actively traded spreads, also narrowed by the most since November 2014 to as low as 60 cents.

"To me, it suggests that the market balances are tighter than what people have believed or generally the consensus has been in recent months," said John Saucer, vice president of research and analysis at Mobius Risk Group in Houston.

Hedging amongst producers has been active, with oil companies taking their biggest short position in U.S. crude futures since the summer of 2007, according to CFTC data, in order to protect themselves against price falls.

Producer hedging has pressured longer-dated contracts, contributing to the narrower spread. In a Sunday note, Goldman Sachs said the hedging activity could cause the rally in those contracts to stall.

There is even a possibility of backwardation in the short term, where later-dated contracts are cheaper than near-term contracts, as the market moves into peak refining season, according to Barclays analyst Michael Cohen.

"We're of the view that the macro and oil specific factors will align to get us into a situation where prices go down at the end of summer. And then, come back up in line with seasonal trends," he said.

Goldman added that the fall in supply happened more quickly than expected, though they expect supply to rebound in 2017.

Hedge funds may play a role in the sustainability of the rally in crude if their appetite for commodities ebbs, taking with it the flow of cash.

Data from the CFTC shows hedge funds reduced bullish U.S. crude oil bets for a second straight week last week, driven by a one-third increase in short selling. Those funds still carry a notable long position in the market, however. (Additional reporting by Catherine Ngai in New York) ((devika.kumar@thomsonreuters.com; +1 646 223 6059; Reuters Messaging: devika.kumar.thomsonreuters.com@reuters.net))