MPs have backed plans to allow some deaths to be investigated by a closed inquiry rather than an inquest jury, despite fears about "secret justice".
MPs voted to overturn amendments made in the Lords to allow intercept evidence to be used in inquests.
Campaigners had hoped that would rule out the need to prevent the details of some deaths being heard by an inquest.
But the government argued using phone tap and bugging evidence would have been a "risk to national security".
A clause in the Coroners and Justice Bill would allow the Inquiries Act to be used to hold investigations into deaths involving information that could not be placed before a jury.
Currently there is only one case where the central evidence was taken from "intercept" evidence - the death of Azelle Rodney, shot dead by police in north London in 2005, as he sat in the back of a car.
Mr Straw said there was "grave anxiety" that intercept evidence would have to be made available to people who were not security cleared.
Campaigners fear details of other deaths - like that of Jean Charles de Menezes, shot by police who mistook him for a suicide bomber - would be kept secret.
It seems like this debate is something of a groundhog day
Last month in the Lords, the government suffered two defeats on the Bill - on secret inquests and the use of intercept evidence - but MPs voted to overturn them.
The Bill now goes back to the Lords with the Commons and peers on a collision course with time running out before the end of the current parliamentary session on Thursday.
On Monday the government's majority was cut to just eight in a vote on an amendment that would have allowed an inquest to continue even if a death was made the subject of a special inquiry.
MPs voted 274 to 266 to defeat the bid, by the Labour MP Andrew Dismore, which had cross-party backing.
Mr Dismore told MPs he had been pleased when the government dropped its original plan for secret inquests earlier this year - only to be disappointed when the new secret inquiries plan was introduced.
"It seems like this debate is something of a groundhog day," he said, adding that the new proposals were worse than the secret inquest plans.
He said the move would mean inquiries held at the behest of the government, which could set their terms of reference, choose a judge, restrict attendance and publication of evidence or suspend proceedings "merely on the grounds that it's in the public interest".
The government dropped plans for secret inquests this year
His Labour colleague Bob Marshall-Andrews said inquiries were a "disproportionate remedy" which would hand "massive new power to the executive".
For the Conservatives, Dominic Grieve said the government faced a "conundrum" but the current proposals were "unsatisfactory" and should go back to the Lords.
David Howarth, for the Liberal Democrats, said the new plan was "in many respects worse" than the original secret inquests plan.
For the government, Mr Straw said only a "tiny number" of cases would be affected and "every effort" would be made to ensure a normal coroner's inquest was used "if humanly possible".
Only senior judges would be able to sit on an inquiry and an appointment could not be made without the approval of the Lord Chief Justice, who would want to look into why it was required, he said.
He admitted he did not like the idea of non-jury inquests but added: "What I'm trying to do here is square an extraordinarily difficult circle and have not yet found any way of doing it except by a route similar to this.
"The alternative of jury inquest from which material would be withheld is not a way of reaching at the truth for relatives."
But Shami Chakrabarti, director of the campaign group Liberty, said the closeness of the vote on Mr Dismore's amendment should make the government rethink its plans.
"The British public has no taste for secret justice, particularly when the rights of grieving families are at stake," she said.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.