The UK's extradition arrangements with the US and the EU must be overhauled to better protect rights of individuals, a committee of MPs and peers is arguing.
It said safeguards in US cases were "inadequate", more evidence was needed to justify requests and judges should be able to refuse them if they were not in the "interests of justice".
High-profile extradition cases, such as that of computer hacker Gary McKinnon, have fuelled demands for a reappraisal.
Ministers are reviewing current rules.
Home Secretary Theresa May ordered the review last year to determine whether the UK's extradition arrangements with the US - in place since 2003 - were "balanced" following a spate of controversial cases.
In a new report, the cross-party Joint Committee on Human Rights said tougher safeguards were needed to ensure individuals' rights to a fair trial and to protect their private and family lives.
It has called for the the 2003 US-UK Treaty to be "urgently renegotiated" to enable the government to refuse extradition requests if UK prosecutors have decided against beginning proceedings at home.
Requests should only be considered if the US authorities provide prima facie evidence that the suspect has a case to answer to prevent people being sent to face trial abroad on "speculative charges", it says.
Although provisions already exist for judges to deny extradition if an alleged offence took place wholly or legally in the UK, the committee said these were not being put into practice.
The committee also calls for the government to renegotiate the terms of the European Arrest Warrant, which came into force in the UK in 2004 to speed up extradition requests between EU member states.
It says there are "serious problems" with how the system is operating, that some warrants have been issued disproportionately and for relatively minor offences.
The BBC's home affairs correspondent Danny Shaw said the committee believed judges did not have enough discretion about how to act in such cases.
Hywel Francis, the Labour MP who chairs the joint committee, said human rights provisions in the Extradition Act were "clearly inadequate".
"The government should spell out detailed safeguards, he said.
"A most appropriate safeguard would require the judge in an extradition case to consider whether it is in the interests of justice for the individual to be tried in the requesting country."
The home secretary is currently reviewing the case of Gary McKinnon, whom the US authorities want to extradite for hacking into Pentagon computer systems in 2001 and 2002.
Mr McKinnon, who suffers from Asperger's Syndrome, faces a potential sentence of 60 years in jail if convicted and campaigners say such a vulnerable person should not face trial in the US on medical grounds.
In its report, the committee concluded that the power of the home secretary to refuse extradition to non-EU countries should not be extended but it should be up to judges to adequately protect an individual's rights.
One leading extradition lawyer said calls for change to a "draconian" system were long overdue.
"Any changes to our extradition procedure should take place without delay," Michael Caplan, from solicitors Kingsley Napley, said.
"We must not lose sight of the fact that we are dealing with the freedom of individuals. If extradited, they are separated from their families, often held in custody in a foreign jurisdiction, alone, many miles from home."
The last Labour government resisted calls for a review of extradition laws, saying they struck the right balance between liberty and security and other countries had to meet the same evidence thresholds as the UK.