The revolt failed after two days of shooting in the capital, Bujumbura, and the generals who led it surrendered.
''I hope they won't kill us,'' the coup leader, Major-general Godefroid Niyombare, said. But like much else in Burundi, that remains up in the air.
Burundi, a small, densely populated country (10 million people) in the centre of Africa, has had a relatively good 10 years.
After a 12-year civil war that killed 300,000 people, a deal was struck at Arusha in 2005 that made the leader of the Hutu rebel group, Pierre Nkurunziza, the president, but divided the army equally between Hutus and Tutsis
It was a messy compromise, since Hutus are 80% of the population and Tutsis only 15%.
However, it avoided the much worse carnage in neighbouring Rwanda, a country with the same ethnic mix, where 800,000 Tutsis and moderate Hutus were murdered in three months in 1994, so it was worth it.
Mr Nkurunziza was appointed president of Burundi for five years (there was no time for an election at the end of a civil war), but he ran successfully for a second term in the 2010 election.
The trouble started when he announced early this year that he intended to run for a third term as president in the election due this June.
The new (2005) constitution says that presidents may only serve for two terms.
The two-term limit became standard in the new democracies that spread across Africa in the 1990s, and by 10 years ago 34 African countries had put it into their constitutions.
It is an attempt to end the ''Big Man'' phenomenon in African politics and make peaceful political change possible, but it does not always work.
In the last quarter-century, 18 African presidents have reached the two-term limit.
Only eight of them stepped down without first trying to amend the constitution and abolish or change the term limit.
As President Mathieu Kerekou of Benin remarked ruefully: ''If you don't leave power, power will leave you.''
But 10 other presidents did try to amend the constitution in order to stay past two terms, and seven of them succeeded.
Moreover, all the presidents who managed to change the constitution also won the subsequent election, most notably Yoweri Museveni of Uganda, who famously said in 1986 that ''no African president should be in power for more than 10 years.''
Mr Museveni has now been in power for 29 years, and is preparing for the next election.
So the glass is at best half-full, although long-serving President Blaise Compaore of Burkina Faso was chased from power by popular protests last year when he tried to amend the constitution to give himself another term.
But here comes Pierre Nkurunziza, who cannot bring himself to stop being president after only two terms.
Burundi is exactly the wrong place to do this sort of thing.
The country's relative peace and modest prosperity depend on everybody being confident that the inter-ethnic killing is really over.
That in turn depends on everybody observing the terms of the power-sharing deal between Hutus and Tutsis worked out at Arusha 10 years ago.
Mr Nkurunziza was already showing signs of dissatisfaction with the deal.
Last year, he tried and failed to change the part of the constitution that guarantees positions for the minority Tutsi group in all government institutions.
His party's youth wing, the Imbonerakure, has recently been given weapons, and its resemblance to the Interahamwe militia that did much of the killing in Rwanda makes many people uneasy.
The first step in his plan for holding on to power was to get the Constitutional Court to decide that he had not really served two terms, because for the first term he was appointed by Parliament, not elected by the people.
The Constitutional Court agreed - although one of its judges then fled the country and said that they had all been bullied and threatened into giving that judgement.
Last month, the chairwoman of the African Union Commission, Nkosazana Dlamini-Zuma, questioned the decision by the Burundi court, saying the Arusha peace accord clearly stated a president should not seek a third term.
More recently the African Union called for the postponement of the Burundi election, at present scheduled for June.
And of course the protesters have been out in the streets of Bujumbura every day, although at least 20 have been killed already.
Even after the failed coup (which they deny any connection with) some of them are still going out to protest.
But Burundi is clearly drifting back towards a civil war, if not an actual genocide.
More than 50,000 people fled the country just last week in fear of what is to come.
The time to put pressure on Mr Nkurunziza to back off and obey the law is now; later may be too late.
It should come above all from African countries and institutions, but it certainly wouldn't hurt if the major providers of aid to Burundi also made their views known loudly and clearly.
• Gwynne Dyer is an independent London journalist.
