U.S. oil prices have rebounded 14 percent from last month's 5 ½-year low of $43 a barrel. But Tom Kloza, co-founder of Oil Price Information Service, doesn't think the plunge is over.

U.S. crude could fall below $40 in the second quarter, he told CNBC.

"I think the cycle has a long way to run out," Kloza said.

While oil bulls have pointed to a decline in rig counts during recent weeks, he is unconvinced.

"It's still about oil shale, and the rig count is very misleading," he noted. He explained that there are about 500,000 wells in this country producing fewer than 15 barrels a day.

"We're going to fill up in storage, and it doesn't appear that there's any way around that. Some of the additional crude oil from the water will come to the United States simply because we have the facilities to store it," Kloza explained.

"The second quarter looks really ugly for crude oil."

Citigroup analysts are even more bearish than Kloza is. They wrote in a report obtained by Bloomberg that prices could slide to the $20 area for "a while," calling the recent recovery a "head-fake."

U.S. oil production has hit an at-least 32-year high. And it's still rising, according to the Citi analysts. Brazil and Russia are producing at record levels, and Saudi Arabia, Iraq and Iran have been cutting prices in Asia to protect their market share. So oversupply abounds, the analysts say.

They don't see production falling back until the third quarter.

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