In terms of convention delegates, the outcome means nothing; only 10,000 votes were cast. But it will damage morale in the Dole camp a week before the first serious candidates' confrontation in Louisiana and less than a fortnight before Iowa holds the caucuses that start the election season.
The winner of the Alaska straw poll was the conservative commentator, Pat Buchanan, with 33 per cent, followed by Steve Forbes, the publishing magnate who is fast emerging as Mr Dole's possible nemesis, with 31 per cent. Mr Dole, who did not personally campaign, scored only 17 per cent.
With Iowa and the crucial New Hampshire primary fast approaching, the aura of inevitability around the Senate Majority Leader's candidacy has vanished. One factor was his dismal response to President Bill Clinton's State of the Union address last week; a second was relentless advertising by Mr Forbes. Most important is the impression that at 72, he is the wrong man at the wrong time.
In New Hampshire the omens are worrying. One survey showed his lead over Mr Forbes slipping from 17 to 11 per cent. On Monday one poll put Mr Forbes ahead, by 29 to 24 per cent. Mr Dole has accused the liberal media of favouring Mr Forbes, whose fortune is put at $450m (pounds 300m). Or maybe, Mr Dole said, "He owns stock in all those networks".