Coroners will be given power to prevent details from high-profile cases such as the Soham murders being reported by the media under government proposals.
Harold Shipman evaded the system for 25 years
Constitutional Affairs minister Harriet Harman said the restrictions would make the inquest process itself more open.
Reporting restrictions would enable cases currently heard in private to be held in public without sensitive details being revealed, she said.
Such restrictions would apply mainly in cases involving children or suicides.
'Under the carpet'
Ms Harman said: "Coroners have told me that when they believe it is not in the public interest, but they need to do a proper inquest, they effectively sit in private and the whole thing is a bit too much under the carpet."
She said the bill would put coroners' courts on the same footing as criminal courts.
"The criminal courts are not secret courts - they sit in public, but they have the power to impose reporting restrictions," she said.
Under the draft Coroners Reform Bill, coroners could ban the media from naming a dead person or publishing information that revealed his or her identity.
People would also be able to ask for a "second opinion" on death certificates under the plans for England and Wales.
The changes come partly in response to criticisms of the system in the wake of the Shipman murders.
Dr Harold Shipman was jailed for life in 2000 for murdering 15 patients while a GP at Hyde, Greater Manchester. He hanged himself at Wakefield Prison in January 2004.
An official report later concluded he killed at least 215 patients between 1975 and 1998.
Radical reform urged
In a joint foreword to the draft Bill, Lord Chancellor Lord Falconer and Constitutional Affairs Minister Harriet Harman described the present system as "fragmented, non-accountable, variable in its processes and its quality, ineffective in part, archaic in its statutory basis, and very much dependent on the good people working in, or resourcing it".
Dr Michael Wilkes, chair of the British Medical Association's ethic committee, told the Today programme the plans were "largely welcome" but did not go as far as the government had been advised to go.
He added: "Everything's going to hang on how much resources are provided for this particular initiative.
"Current procedures would have detected Shipman had they had the resources given to them to join them up."
When the government previously outlined the plans, Dame Janet Smith, chair of the official inquiry into the Shipman killings, said they would not prevent a similar case in future.
Ms Harman said the new laws would help families
Dame Janet's report in 2003 suggested there should be radical reform of the coroners' courts as well as the registration of deaths and cremation to better detect cases of murder, medical error and neglect.
Shipman had managed to evade scrutiny by saying his victims had died of natural causes.
Solicitor Ann Alexander, a lawyer for relatives of the victims of serial killer Dr Harold Shipman, said proposed changes were "well overdue" even if the bill did not address all concerns.
She said: "Shipman was a doctor who avoided the law whilst murdering his patients by exploiting all the loopholes in the current system.
"This bill will go a long way to close one of these loopholes, but others remain."
However, North London coroner Dr William Dolman, who is the busiest coroner in England and Wales, said he could not think of any situations in which the new powers should be used.
"In all my years on the coroner's bench, I don't think I have ever had to have the secret inquests that have been referred to," he said.
"It must be a very rare occasion."
The existing coroner's system in England and Wales can trace its roots back 700 years.
The draft bill also proposes:
The existing 111 mostly part-time coroners be replaced with 65 full-time posts.
A system for appointing and training coroners.
A new chief coroner directly accountable to ministers.
The bill is the first to be published with a "plain English" explanation alongside the legal text.