After a dramatic few days that saw oil prices plunge before zero for the first time in history, crude continued to claw back losses and was on track to close out the week not far from where it started.

Futures in New York rose for a fourth day to above $17 a barrel, paring their loss for the week to around 6%, as attention shifted to output cuts in response to the demand destruction caused by coronavirus lockdowns. US operators have already started to shut in old wells and halt new drilling, actions that could reduce output by 20%, while Kuwait and Algeria said they are reducing production earlier than required to under the OPEC+ deal.

The massive glut won’t be cleared quickly, however, meaning West Texas Intermediate and even global benchmark Brent crude are still at risk of further declines. In a sign of how severe the supply imbalance is, refiners are hunting for vessels to store gasoline and jet fuel, while an American pipeline operator is looking at ways to free up space on its conduits to store more crude.

With still no clear indication of when demand might recover, the market is set for a prolonged slump that will reshape the industry for years to come. Oil’s collapse will be followed by the weakest recovery in history, according to the World Bank, while consultancy Rystad Energy revised down its demand estimates for a fourth time since early March.

WTI crude for June delivery rose 5.3% to $17.37 a barrel on the New York Mercantile Exchange as of 8:32 a.m. in Singapore. The May contract plunged to a record low -$40.32 on Monday. The premium of the December contract over June narrowed from higher than $15 earlier in the week, indicating concern over the glut is easing slightly.

Brent crude for June settlement climbed 4.2% to $22.23 a barrel on the ICE Futures Europe exchange after advancing 4.7% on Thursday. It’s down 21% so far this week.

Oil markets are also having to grapple with a wave of volatility spurred by exchange-traded funds. At least four brokerages — including INTL FCStone Financial Inc. and Marex Spectron — are restricting the ability of clients to enter into new trades in the most active oil benchmarks in a bid to curb losses.

Producers and refiners are also starting to declare force majeure in what could be a wave of broken contracts. American shale explorer Continental Resources Inc. told at least one refiner it couldn’t make an oil delivery after the price rout, while the trading unit of Petroleos Mexicanos said it couldn’t import gasoline from at least one U.S. company.