NEW YORK (

TheStreet

) -- Crude oil futures traded above and below the flatline during a jerky Tuesday trading session as observers awaited demand data illustrating last week's inventory picture.

The crude oil contract for May delivery was recently adding a penny at $81.61 a barrel, though the contract slipped to $80.85 at one point. On Monday, the contract gained 63 cents, or 0.8%, to settle at $81.60 a barrel.

A stronger greenback was putting pressure on the contract in the morning, capping any definitive price moves. The dollar index, which measures the buck against a basket of currencies, was adding nearly 0.2%.

But investors will be eyeing supply figures over the next 24 hours, with the American Petroleum Industry's weekly snapshot scheduled for release after Tuesday's closing bell and the government's Energy Information Administration report due Wednesday at 10:30 a.m. EDT.

The coming summer driving season means more focus may be put on fuel stocks this week. A survey of Platts analysts says gasoline inventories probably fell by 1.88 million barrels last week, while distillate stocks saw a 1.25 million barrel withdrawal. But those same analysts predict crude inventories jumped by 1.67 million barrels.

"Crude supplies are expected to show a small increase largely as a result of an expected uptick in imports of as much as 100-150,000 b/d per the EIA," said Jim Ritterbusch, independent analyst, in a Platts release.

Refinery operations probably slowed last week. If expectations hold, the refinery run rate will slip 0.12% to 80.48%.

The

U.S. Oil Fund

(USO) - Get Report

ETF was holding flat. The

PowerShares DB Oil Fund

(DBO) - Get Report

gained 0.1%.

Oil-related equities were moving in-kind with commodity prices, as the New York Stock Exchange Arca Oil index fell off by 0.3%. The Philadelphia Oil Service Sector index slid 0.1%.

The major integrated firms were trading broadly lower. Shares of

Exxon Mobil

(XOM) - Get Report

,

Chevron

(CVX) - Get Report

and

ConocoPhillips

(COP) - Get Report

were off by 0.6%, 0.4% and 0.4%, respectively, though

Occidental Petroleum

(OXY) - Get Report

was improving 0.3%.

Elsewhere on the Nymex, April natural gas gained 3 cents at $4.11 per million British thermal units. April heating oil traded nearly a penny higher to $2.09 a gallon, while April gasoline slipped a fraction to $2.25 a gallon.

--Written by Sung Moss in New York