Even without knowing the details of IAG SA’s offer to acquire Norwegian Air Shuttle ASA, it’s little surprise that the budget transatlantic carrier has rejected it.

IAG boss Willy Walsh, a pretty canny operator, would have been aware that trying to buy Norwegian wouldn’t be easy given its odd governance and shareholder structure. But it’s hard to see at this point how British Airways-owning IAG and Norwegian might settle on a fair price. Walsh should pause to reassess, and maybe the savviest option is to leave Norwegian to settle its own fate.

It’s up to Norwegian’s seven-person board to consider the merits of any offer. Although their decision to reject two separate proposals from IAG was “unanimous,” their independence looks a bit questionable. Chairman Bjorn Kise is a co-founder of Norwegian and together with CEO Bjorn Kjos controls more than one-quarter of the shares.

While Kjos isn’t on the board, three other members are staff representatives, and it’s doubtful that they’d welcome IAG as new owners either: Walsh is a renowned cost-cutter. Curiously, the board’s statement on Friday didn’t invite IAG to return with a higher offer.

But how could the two sides go about assessing fair value anyway? Before the news that IAG had amassed a 4.6 percent stake, Norwegian’s high cash burn had caused its market capitalization to shrink to just 6.9 billion kroner (722 million euros).

After Bloomberg News reported IAG’s interest, the shares shot up 75 percent. Now, after confirmation that Norwegian has rejected IAG’s advances, the stock remains about 50 percent higher than it was before. Kjos has also stoked speculation about rival bids though none has been forthcoming so far.

IAG would surely argue that’s already an ample premium. While he can afford to loosen the purse strings a bit, Walsh’s shareholders would probably be aghast if he agreed to pay much more than 1.5 billion euros for Norwegian’s equity – a level it’s never exceeded. Its market value is about 1.24 billion euros at present, so there’s not much room for a knock-out premium.

Kjos does, however, seem convinced that Norwegian will get over its spending hump this year and everything will be fine. Hence, Norwegian and its fleet of modern fuel-efficient aircraft, are hugely undervalued by his reckoning.

So what should IAG do? A plausible option would be simply to sell the Norwegian stake, book a small but tidy profit and tell Norwegian it remains open to a deal if it changes its mind.

“IAG has no need to make a deal at any price,” says Daniel Roeska at Bernstein Research. “If Norwegian’s board is reluctant the chances of success are slim.” Norwegian has tons of debt and off-balance sheet lease liabilities and if Kjos’s optimism is dashed there’s a chance it will get into more serious difficulties. Walsh told analysts on Friday that Norwegian couldn’t execute its strategy alone.

True, Kjos could end up proving Walsh and bearish investors wrong, in which case IAG will have missed a chance to shap up an emerging transatlantic rival. But minority shareholders relying on Norwegian’s board to look out for their interests are taking a gamble. If IAG does turn its back, they’ll be flying alone.