True, things are beginning to hot up. On Friday, the Takeover Panel dealt not a horsewhipping but a slap on the wrist to Lasmo, which had accused Enterprise of breaching UK accounting rules. Lasmo was told not to make excessive or emotive claims.
But the fight remains reasonably good-natured. This may have something to do with the fact that the two protagonists, Graham Hearne of Enterprise and Rudolph Agnew of Lasmo, are old chums, their friendship forged shooting pheasant together. Mr Agnew, who in previous bid defences has not been afraid to call in private detectives and trade insults, has kept it clean and polite this time.
The bid timetable has now reached a crucial stage. Lasmo has until Friday to issue its final defence document. Then Enterprise has a further week in which to increase its offer. All the signs are that it cannot win without doing so. Its initial all-paper bid - a curious mixture of second-class shares and warrants - has not impressed Lasmo's institutional shareholders one bit.
Enterprise has failed to convince Lasmo shareholders of the merits of its offer. Mr Hearne's insistence that size is essential in oil exploration has backfired cruelly. He has come across as an oil megalomaniac, pursuing size for its own sake. Few people have been convinced there is much synergy in binding the two businesses together.
Actually there is some synergy. But Enterprise has failed to put its message across. Successful exploration is all about accumulating and interpreting information - crunching seismic and drilling data. Build up a strong patchwork of information about a drilling territory and you gain a distinct advantage over competitors. Take the North Sea. It was Enterprise's knowledge about the Forties and Arbroath fields that enabled it to take an educated gamble that an unexplored area between the two might prove fertile. The Nelson field proved a highly lucrative find and is largely the reason for Enterprise's reputation today.
Even on the question of management quality, Enterprise has not entirely routed Lasmo. The defending company, though still stuffed with many of the managers who landed it with all its past woes, has stressed the new blood on its board.
Joe Darby, chief executive, also understands the wisdom of openly confessing past mistakes. Moreover, the City, having reluctantly bailed out Lasmo with its rights issue, is now in some sense emotionally tied to it.
Meanwhile, Lasmo has successfully turned the spotlight back on Enterprise, powerfully suggesting that its record has not been quite as great as generally assumed. Since the Nelson coup, Enterprise's successes have been dwindling and its discovery costs rising. The company may well be paying out too much in dividends. And the shock troops from the glory days of the mid-1980s are disappearing fast: only Mr Hearne remains among the key managers.
Even though the Takeover Panel reprimanded Lasmo over its allegations of accounting irregularities, the blow hit home. It is unarguable that Enterprise has not used the most conservative accounting treatment and that reported profits have been flattered.
So what next? The betting in the City is that Mr Hearne will raise the value of his offer modestly, and sweeten it by offering a bit of cash instead of those unpopular warrants.
That may not be enough. The comparative recent strength of the oil price tends to favour the more highly geared Lasmo. Then there are the US investors who have climbed on to Lasmo's shareholder register over the last 12 months. Now holding more than 20 per cent of the equity, they've already enjoyed a great ride and will not be soured by Lasmo's past mistakes. Lasmo will always go for a price. Shareholders have nothing much to be loyal about. But it is not going to go cheaply.
It has been a sorry tale for Enterprise. Mr Hearne should have shot the bird dead with his first barrel. But he pulled the trigger too late and then missed by a mile. The wise course would be to walk away with the second barrel undischarged. It will be fascinating to see whether, with the scent of blood in his nostrils, he has the necessary self- discipline.