ExxonMobil (XOM) - Get Report is yet reveal its hand as it puts together a rival offer to Oil Search's $2.2 billion bid for Papua New Guinea-focused gas explorer InterOil (IOC) , but it already appears to hold most of the aces.

InterOil on Tuesday said that due diligence by an unnamed bidder, which sources have identified as Exxon, was ongoing and that its lawyers and advisers were still reviewing the non-binding offer.

The target also reiterated its support for the existing Oil Search offer, and set out its case for backing the bid of 8.05 Oil Search shares for each InterOil share.

The rational boiled down to three points: that the bid offered a premium at the time it was made; that it offers upside in the form of contingent value rights for further gas discoveries at the key Elk-Antelope field; and that shareholders might own as much as 21% of the combined Oil Search and InterOil.

The first point is moot. Shares in NYSE-listed InterOil closed Monday $47.40, a 13% premium to the implied price of Oil Search's offer of 8.05 shares, or A$54.74 ($41.73).

Even if ExxonMobil were to simply match Oil Search's offer, which is unlikely, it would have the advantage of offering U.S. stock. IntertOil's listing on the New York Stock Exchange means that its shareholder register is heavily weighted to U.S. investors, many of who are unlikely to appreciate being shunted onto the Australian Securities Exchange via Oil Search's bid.

Oil Search is offering InterOil shareholders the option to take their stock in American Depository Receipts. That would work up to a point, though the contingent value rights, which are a key part of the offer, will still be listed only on the Australian exchange, lessening their attraction to U.S. investors.

ExxonMobil is also better positioned than Oil Search to squeeze extra synergies out of a deal, giving it room to factor such savings into an offer. The U.S. giant operates and owns 33.2% of PNG LNG, an onshore gas field located near to the somewhat confusingly named Papua LNG project, whose key asset is the Elk Antelope field. InterOil owns 36.5% of that field and would have the same stake in the Papua LNG project.

Papua LNG will cost $10 billion to $15 billion to build, depending on whose estimates you use, while a planned extension to PNG LNG will cost about $9 billion. A combination of the two projects, which will anyway share pipelines, could cut those costs by about 10%, according to UBS.

Oil Search's bid for InterOil is underpinned by the strategic rational of that combination. Yet the would-be unifier will remain completely reliant on the operators, Exxon for PNG LNG and Total  (TOT) - Get Report for Papua LNG, to deliver the savings it is touting.

ExxonMobil's ability to turn the screws on the cost savings likely explains why it may be about to offer as much as 10% more than Oil Search, according to a Monday report in the Australian Financial Review, which didn't cite sources.

That leaves only the dubious benefit of InterOil shareholders ending up with between 14% and 21% of Oil Search post deal. The actual amount depends on how many opt for a cash option that is capped at $700 million.

It is true that an ExxonMobil all-share offer would leave InterOil shareholders with a fraction of the U.S. giant, which has a market capitalization of $392 billion. It would also dilute to nearly zero the the potential upside of exposure to Papua New Guinea's gas, which would become lost as just another diversification in ExxonMobil's vast operations.

But the only way that the stake in Oil Search offers significant upside to Inter Oil shareholders is if the bidder is effectively underpaying for its acquisition. And even then there potential upside is diluted by the deal.

None of that implies that the Oil Search bid is not a good offer or unworthy of InterOil's support. But it may turn out that the main thing that it has going for it is that ExxonMobil is yet to make its bid.

And the clock is ticking on that. InterOil shareholders are due to vote on Oil Search's offer on July 28.