A quiet consensus appears to be coalescing in the oil market, as some traders now expect mild gains for crude through the summer— and into the rest of the year.

That represents a sharp turnaround from earlier in the year, when surging U.S. production, and OPEC's powerlessness to stop it, sent crude reeling. Although is off by nearly 40 percent year to date, prices have rebounded significantly enough for market players to expect those gains to continue.

"I'm looking for it to trade $65, $70 by the Fourth of July, and I don't think the market gets much above that," said NYMEX-based energy trader Anthony Grisanti.

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In Grisanti's view, summer demand for oil products is set to drive the commodity higher. At the $70 level, however, an increase in supply from those who have slowed production will cap the commodity's gains.

The same level is being eyed by Phillip Streible, a Chicago-based futures broker with RJO Futures.

"The continued decline in production provides an opportunity that will present itself from now till the end of the year," he told CNBC in an e-mail. "I would expect crude oil to work its way back up to $70."

Brian Stutland, another Chicago-based trader, echoed that sentiment.

There's "a bull pattern in oil, but I think $65 to the upper 60s range is probably the top," he said. That price will send suppliers "coming back in and flooding the market. So there's a lot of overhang at that level, and I'd be a seller up there," Stutland added.

However, "below $60 a barrel, I'm a buyer, and I think the trend for the rest of the summer will be slightly to the upside for crude."