Oil edged further above $37 a barrel on Thursday but remained within sight of an 11-year low reached this week, as signs of a tighter U.S. market raised hopes a supply glut will ease.

U.S. crude has gained support from falling inventories, reduced drilling and the lifting of a ban on most U.S. crude exports, which has pushed U.S. crude to a premium to global benchmark Brent for the first time in about a year. CL-LCO1=R

Brent LCOc1 was up 13 cents at $37.49 a barrel as of 1307 GMT. It fell to $35.98, an 11-year low, on Tuesday. U.S. crude CLc1 was up 20 cents at $37.70 after gaining more than 8 percent this week.

"The lifting of the ban on U.S. exports will provide some underlying support for U.S. crude. Oil demand in 2015 was exceptionally high and at current prices, demand is going to remain strong next year," said Olivier Jakob, analyst at Petromatrix.

"For now, there is still an ample supply of crude and a huge amount in storage."

Brent traders in London said the market was quiet with many participants away for the Christmas holidays.

Crude gained support from the latest snapshot of U.S. supplies on Wednesday. Crude inventories, which were expected to rise, fell 5.88 million barrels, the Energy Information Administration said. [EIA/S]

Baker Hughes reported that U.S. oil drillers cut rigs for a fifth week in the last six, a sign that low prices are curbing activity and could slow output.

Brent has more than halved from over $100 a barrel 18 months ago, pressured by a supply glut that according to OPEC figures is currently over 2 million barrels per day.

Next year, the glut is expected to be smaller as world demand rises and the price collapse leads to lower output from some countries outside OPEC, but there is no sign yet that OPEC itself is prepared to lower its supply - which is likely to rise when sanctions on Iran are lifted.

"While the crude rebalancing should start next year, the pace of inventory drawdown will depend on OPEC output," said analysts at Energy Aspects in a report.

"Despite Iran's return, we believe the cash-strapped OPEC countries will struggle to maintain output, resulting in stronger prices and timespreads in the second half of 2016."