BHP is “disappointed” that its second takeover offer for mining rival Anglo American has been rejected, but it cannot be surprised. The improved terms in the all-share proposal took the headline price from £31bn to £34bn but, since almost everybody agreed the original offer was several mineshafts short of full value, even a £3bn uplift wasn’t enough to put the defending board under serious pressure.

The problem here for BHP is twofold. First, the advertised offer price of £27.53 for Anglo (the day-to-day value obviously fluctuates with BHP’s share price) may look pretty against the pre-action level of £22-ish, but we’re talking about long-life assets here. Anglo stood at £36 in January last year and, if only it could fix its current production headaches, it’s not too hard to imagine it getting close to that level in reasonable time under its own steam. Some outside assistance in the form of a pickup in the price of platinum would help, for starters.

The second issue is the complex structure of BHP’s offer. It requires Anglo to demerge its two big South African units, one in platinum and the other in iron ore, which already have separate listings in Johannesburg. Only then would BHP’s offer for the bulk of the company – stretching from copper mines in Peru and Chile to metallurgical coal in Queensland to De Beers diamonds – proceed.

The proposed model can be presented by BHP as politically savvy, since it would mean South African assets staying under local ownership, but from the point of view of Anglo’s shareholders a two-part transaction just looks messy. All the risk in securing a regulatory thumbs up for the South African demergers sits with Anglo, and there could be a hefty tax bill (some estimates say $2bn (£1.6bn)) at the end of the process.

There will, of course, still be a takeover price at which Anglo’s board would be obliged to roll over and say the risks and uncertainties are worth accepting. Anglo’s current structure, after all, is hardly simple; and the benefit of a combo with BHP would be the bidder’s undoubted ability to ramp up investment. But logic still says the take-out price should involve more than just a conventional premium to compensate for the fussiness of the takeover structure. At the moment, BHP’s offer is just not in compelling territory.

None of which gives Anglo’s board a free pass. The parallel promise from its boardroom on Monday was that the “accelerated plans” for a standalone future would follow on Tuesday. There’s nothing like a bid to accelerate a board’s thinking, but chairman Stuart Chambers needs to have something substantial to say, beyond a predictable promise to boost production.

A good start would be to find some assets to sell to show the value within Anglo – some analysts suggest a prime candidate would be iron ore in Brazil. Whatever it is, the takeover defence needs to move the dial on shareholder expectations. Given the performance for investors over the past decade has been a series of disappointments, a pledge to carry on doing the same thing ain’t going to cut it.