There is, of course, an innocent explanation: these three prominent Republicans are doing their bit to secure the tricky re-election of George Bush. But nobody is fooled: these are the opening moves in the battle for the party nomination in 1996.
Mr Bush was nominated only last night, but the jockeying for his succession has started. Good taste and political prudence rule out public admission of such ambitions. Unlike 1984, when Ronald Reagan's second term was a certainty, and 1988 when Mr Bush could contemplate eight years in the White House, this is a Republican party whose future stewardship is anything but certain.
Mr Quayle, Mr Kemp and Mr Gramm are the most obvious contenders. Pat Buchanan, who caused Mr Bush so much difficulty in the early primaries, is expected to throw his hat into the ring. So may the Defence Secretary, Dick Cheney, and even Mr Bush's old buddy James Baker. And where better to lay the groundwork than at the party convention?
Iowa and Hampshire are sites of the first primaries which can make or break a presidential candidacy. The religious right and the farm lobby are key parts of any Republican coalition. Mr Kemp, who ran against Mr Bush in 1988, is an economic conservative who - almost alone in the administration - is a crusader for America's battered cities.
He is leading the pack. A poll of delegates on their 1996 preferences showed a third favouring Mr Kemp, 10 per cent Mr Quayle, with the remainder in low single digits. Mr Kemp's convention speech did him no harm, but Mr Gramm's was a disappointment.
As for Mr Quayle, the Republicans have to win in November if he is to remain a serious contender. But tonight in his acceptance speech, he must prove he is more than a butt for comedians. The figures themselves mean little, but they show that the most visible contenders come from the party's conservative wing.
Moderates, among whom Mr Bush was once numbered, are hardly to be seen. Nearly a third of Republican senators and congressmen, upset by the right wing's grip on the convention, stayed away. Of their prominent spokesmen, only Governor William Weld of Massachusetts has so far spoken from the platform - gaining as many boos as cheers for daring to oppose the draconian anti-abortion plank in the platform.