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NEW YORK (CNNMoney.com) -- Crude closed at $33.87 a barrel earlier this winter, and that's likely the lowest we'll see for some time.

Oil prices crossed the $50 a barrel mark Thursday, the first time since early January. Thursday's uptick is largely due to the falling dollar, but the underlying fundamentals in the oil market indicate low prices are behind us.

While demand remains abysmal, production cuts from OPEC and scaled-back investments from oil companies are beginning to curtail supplies.

That, say analysts, means crude prices won't likely trade below the $40 range they've been locked in for the last three weeks.

"OPEC cuts are taking hold," Adam Sieminski, chief energy economist at Deutsche Bank, wrote in a recent research note. "Looking into the second quarter we believe oil prices are starting to find a floor."

OPEC has been ratcheting back production since late last year. While the cartel often has trouble making some cash-strapped members actually comply with the production cuts, this time around nearly everyone is on board.

OPEC has announced production cuts totaling 4.2 million barrels a day, and is thought to have achieved at least 80% of that so far, according to the research firm Platts.

Production in non-OPEC countries has also tightened, as deteriorating economic conditions force companies to cut back their exploration and production efforts.

All this is beginning to show up in U.S. inventories.

During the first part of the year, crude oil stored at refineries, tank farms and other places in the U.S. soared, often swelling by 5 or 6 million barrels a week, according to the government's Energy Information Administration.

Now those gains have been cut way back. Wednesday showed a gain of 2 million barrels, but the week before inventories dropped by 200,000 barrels.

"All these are signs that the physical market is tightening," said Nauman Barakat, an energy trader at Macquarie Futures, the trading arm of Macquarie investment bank.

Demand is the other side of the oil price equation.

At first glance the numbers seem terrible.

February demand for oil in the U.S. was at its lowest level since 1999, according to the American Petroleum Institute.

Diesel, used in trucks and trains, was particularly hard hit as freight shipments have been slashed during the recession, dropped a staggering 12%, according to API.

But that's not the whole story.

Gasoline demand in the U.S. actually rose 2%, which API said may be attributed to lower gas prices.

And overseas much has been made of China's drop in oil imports. But Barakat said those numbers may be misleading, as they compare to a period last year when the country was stockpiling oil ahead of the Olympic games.

"You could make a compelling case for stability, maybe even higher prices" in the coming months, said Paul Smith, chief risk officer for Mobius Risk Group, which secures energy contracts for producers and users of oil.

But if prices may creep higher over the next several months, no one is calling for a return to last summer's record prices anytime soon.

First off, when OPEC decided to hold off on another production cut at its meeting last weekend, analysts took it as a sign that the cartel is keen to keep prices low to protect the economy.

"Leading OPEC members, particularly Saudi Arabia, do not want to risk - even if a low probability - a potential over-tightening of production which could send prices quickly back above $60 per barrel," Greg Priddy, global oil analyst at the consultancy Eurasia Group, wrote in a research report earlier this week.

But more important is the amount of capacity the world now has. When oil passed $147 last summer, the difference between what the world could produce and what it consumed had narrowed to 1 or 2 million barrels a day.

That narrow margin brought geopolitics into play, as a supply disruption from one part of the world would mean there may suddenly be a shortage of oil.

The specter of an actual shortage - and the surge in prices that would surely follow - attracted investors, who at the time could borrow vast sums of money and push prices even higher.

A return to all those conditions is needed before anyone thinks crude will test those old highs. Most importantly, that margin of production must return to the 1 or 2 million barrels a day range from its current fluffy cushion of 4 or 5 million barrels a day.

For that to happen, the world's economy needs to start humming again.