Seymour eyed American exploration and production names on the potential for more supply. He believes Hess and Anadarko Petroleum have particularly strong balance sheets and can withstand choppy oil trading.
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Hess closed barely positive on Thursday, while Anadarko climbed nearly 1 percent.
Trader Guy Adami looked to Tesoro, an American refiner rather than producer. Tesoro has jumped about 17 percent this year as the spread between U.S. WTI crude and Brent sits at about $6 per barrel.
Tesoro shares fell more than 5 percent Thursday, and Adami believes the drop offers a good entry point.
A sustained high supply environment will benefit tanker stocks, said trader Karen Finerman. She noted that shipping company Navios looked appealing after it "popped up nicely" on Thursday.
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Shares in Navios closed nearly 6 percent higher on the day.
Individual stocks are likely a risky way to play oil, trader David Seaburg said. He eyed the SPDR S&P Oil and Gas Exploration and Production ETF, which climbed more than 1 percent on Thursday.
Tim Seymour is long T, BAC, C, DIS, F, GE, GM, GOOGL, INTC, LO, EWZ and SUNE. Tim's firm is long BABA, BIDU, MCD, NKE, NOK, SBUX and YNDX.
Karen Finerman is long BABA, BAC, C, FINL, FL, GOOG, GOOGL, JPM, M, KORS, she is short DIA, her firm is long ANTM, AAPL, BAC, C, CMLS, DIS, FINL, FBT, FL, GOOG, GOOGL, IBB, JPM, M, OIH, KORS, XBI, SUNE, URI, her firm is long calls URI, her firm is short IWM, SPY, USO, Karen Finerman is on the board of GrafTech International.
Guy Adami is long CELG, EXAS, INTC, Guy Adami's wife, Linda Snow, works at Merck.