Stock markets in the U.S. are up again today as the freeze in Washington, appears to be thawing. Senate Republicans met with President Barack Obama at the White House today, and there appears to be dialogue between the two sides. No deal either to reopen the government or to increase the debt ceiling is done, but there appears to be hope ahead of the Thursday deadline to avoid debt default.

Most stock indexes rose on the reports from Washington, and late in today's session, the Dow Jones Industrial Average (^DJI 0.69%) is up another 0.57% after its biggest day of the year yesterday.

Oil prices fall -- and that's a good thing?
One notable move on the Dow is in oil stocks. Oil is down 1.2% today, but big oil stocks are actually outpacing the average as a whole. What's going on?

The International Energy Agency released its monthly report, predicting that oil demand will rise by 1 million barrels per day this year, above the previous estimate of 900,000 barrels. Projected growth of 1.1 million barrels for 2014 stayed flat, but with this year's growth, demand will be higher than previously predicted overall.  

As a result, ExxonMobil (XOM 0.39%) and Chevron (CVX 0.57%) in total should see more demand this year and next. That's why their stocks are up about 0.9% each despite the drop in oil prices. Higher overall demand is good for both companies; while they make less money on exploration, lower oil prices can boost refining margins, which have been squeezed recently.

The other positive for ExxonMobil and Chevron is that OPEC is accounting for less supply. The IEA said OPEC supplied 645,000 barrels per day less last month than the previous month, but other countries are picking up the slack. That's an opening for both companies, which have operations around the world.

How to play the oil market now
The big trends in the oil industry over the past decade has been away from traditional sources and toward formerly inefficient sources of supply like shale oil and ultra-deepwater offshore drilling. Chevron has been a big player in ultra-deepwater, while ExxonMobile bought XTO Energy in 2009, partly to expand unconventional oil reserves. But investors should look outside of Big Oil for more upside in the industry.

I think the biggest opportunity is in offshore drilling, particularly in ultra-deepwater. This is where Transocean (RIG 2.24%) and Seadrill (SDRL) have dominant positions and don't take risk on each oil well the way ExxonMobil or Chevron do. Transocean has the largest deepwater fleet in the industry, while Seadrill has the newest fleet and is expanding aggressively.

Neither company benefits directly from high oil prices or high oil demand, but both see higher rig demand when prices and demand go up. They also sign long-term contracts with explorers, including ExxonMobil and Chevron. That makes them a more stable and more profitable way to play oil trends right now.