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."

After a massive plunge and a substantial bounce-back, the international Brent contract has currently settled into a comfortable range between $55.73 and $66.58 over the past month.

Yet over the last two weeks, that has further narrowed into a $4 range. Meanwhile, the crude oil volatility index, which uses options prices to measure market expectations of future moves, has been halved since the start of February.

Meanwhile, the crude oil futures curve has become much flatter recently, meaning that the expected magnitude of the oil bounce has diminished. Currently, crude oil futures for December delivery are trading at a mere 2.5 percent premium to the front-month July contract.

Yet not everyone forecasts a mild grind higher for the commodity. Last week, Goldman Sachs turned bearish on commodities, forecasting that West Texas Intermediate (WTI) oil contract would "retrace its lows" near $45 before staging a recovery.

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"Oil demand typically peaks in late July or early August, but refineries are running at such a record pace that we're stealing demand and moving it forward," said Stephen Schork, the editor of the Schork Report. Refiners are seeing high profit margins based largely on gasoline outperforming crude.

"I'm looking for demand to start tailing off earlier than normal—in late June or early July—which supply stays robust," he said. "Put those two factors together, and I think we do head lower—that's just Econ 101," Schork said.

"I'm looking for another dip below $50."

—By CNBC's Alex Rosenberg.

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