Oil futures jumped nearly $3 a barrel Tuesday morning on optimism that European leaders were finally making significant headway in addressing the sovereign debt crisis.

The sharp rise countered heavy selling in recent days and gave hope to traders hoping for a floor at the $80 level. Traders said some of the buying appeared to be driven by the need to cover short positions taken on as market sentiment became bearish in recent days.

"Risk-on, risk-off...and risk is back on again," Summit Energy analyst Matt Smith said in a research note Tuesday morning.

At 8:55 a.m. EDT, prices had fallen back somewhat, with light, sweet crude for November delivery up $2.25, or 2.85, to $82.49 a barrel on the New York Mercantile Exchange. Brent crude on the ICE Futures Europe exchange was up $1.46, or 1.4%, at $105.40 a barrel.

Prices followed equity and commodity indexes higher on reports that European officials are developing a plan to expand euro-zone bailout funds. Speculation that the European Central Bank will inject more liquidity into the banking system or cut the bank's key interest rate at its October's policy-board meeting also helped improve sentiment.

"We're just seeing a little bit of a recovery in commodities overall, with gold and equities here," said Fred Rigolini, a vice president at Paramount Options. "There's a lot of short-covering. There was a pretty decent amount yesterday and some follow-through today. Right now that's one of the factors driving the rally."

Also driving the trend was the strengthening of the euro against the dollar, with the ICE Dollar Index down 0.3%, to 77.800. A weaker dollar can drive oil prices up, as it makes the dollar-denominated commodity a more attractive investment for holders of other currencies.

Analysts have also been watching developments in Libya, with production restarting as the civil strife there winds down. The country's deputy oil minister said Monday that it is expecting to ship its first crude exports Tuesday since the toppling of Col. Moammar Gadhafi.

"The market has had these elements in front of it for weeks or months, long enough that they should have been discounted into the price," Citi Futures Perspective analyst Timothy Evans said in a recent research note. "This fits with the contention that even with economic slowing there is still enough demand growth to carry prices higher. That is the theory at any rate."

In a research note, Barclays Capital said it expects oil to outperform other commodities in the near future, as "healthy demand data" and "the deteriorating profile of supplies" should support prices, even though traders appear focused on bigger macroeconomic concerns at the moment.

"Such is the extent of the contrast in the paper market which faces strong and frequent gusts of sell-offs and widespread derisking," the bank said.

Front-month October reformulated gasoline blendstock, or RBOB, recently traded up 6.66 cents, or 2.59%, at $2.6360 a gallon. October heating oil was up 4.24 cents, or 1.52%, at $2.8339 a gallon.