Who should decide whether a suspect should be extradited to stand trial abroad? Is extradition purely a legal matter, to be decided by the courts? Or should ministers have the discretion to block extradition in appropriate cases?
Lawyers and MPs have been considering these questions since Theresa May decided last month that Gary McKinnon would not be extradited to the United States.
The Home Secretary told MPs that sending him to face trial on charges of hacking into US government computers would pose such a risk to his health that it would be incompatible with his human rights - Gary McKinnon has Asperger's syndrome and suffers from a depressive illness.
But until the law was changed in 2003, a suspect could not be extradited from the United Kingdom without approval from both politicians and the courts.
That was how Jack Straw, as a Labour government Home Secretary, was able to block the extradition of Augusto Pinochet to Spain, where a prosecutor wanted to put the former Chilean dictator on trial for human rights abuses.
The UK's highest court had decided that Pinochet's extradition would be lawful, but Jack Straw intervened early in 2000, concluding that General Pinochet, like Gary McKinnon, was too ill to face legal proceedings abroad.
However, new legislation was then passed in 2003 to remove the Home Secretary's discretion in extradition cases.
It followed concerns that suspects were dragging out cases and avoiding extradition by challenging ministerial decisions in the courts - and there was also a perception that ministers were influenced by political factors in deciding whether or not to approve extradition.
Human Rights Act
So, the 2003 Act posed something of a problem for Theresa May when she came to consider Gary McKinnon's case.
His extradition had been ordered by the courts. But the Home Secretary was concerned that he might take his own life if he was sent for trial in the US - and yet she did not have a general discretion to block extradition, as Jack Straw did in the Pinochet case.
The Human Rights Act provided her with a solution - all ministers are bound by it. Theresa May looked at the medical evidence and concluded that Gary McKinnon's health had deteriorated since he had last appeared before the courts.
That led her to conclude that extradition would be incompatible with article 3 of the European Convention on Human Rights, which says: "No one shall be subjected to torture or to inhuman or degrading treatment or punishment."
But, having taken the decision, Theresa May decided that "the breadth of the Home Secretary's involvement in extradition cases should be reduced".
She announced that any representations on human rights grounds should, in future, be considered by the High Court rather than by the Home Secretary.
It is this decision that has divided two leading MPs, speaking on BBC Radio 4's Law in Action.
The former Conservative Solicitor General, Sir Edward Garnier QC MP, said he would retain ministerial discretion in extradition cases.
"I would have kept it within the political sphere because I think the political sphere is better able to respond to day-to-day events," he told the programme.
"And justice does need to reflect changing circumstances."
A human element
Sir Edward, who was the government's second most senior law officer until he lost his job in the reshuffle two months ago, accepts that not having to take decisions on extradition in individual cases might make the Home Secretary's life easier.
"But it will make the system slower and it might make the system less responsive to the needs of a particular case," he adds.
"Whilst a politician will, when approaching a question like this, have to deal with it in a quasi-judicial fashion - the minister can't behave irrationally - he or she can add in that human aspect which a judge, perhaps, would feel unable to do."
Essentially, there is no point in putting opinion polls before judges.
"They [judges] will have to look at the facts, look at the law and apply the one to the other - end of.
"Theresa May, as Home Secretary, does all of that, but she can add an additional factor which it is entirely legitimate, in my view, to bring into these sorts of decisions."
But the Home Secretary's decision to hand over her new-found discretion to the courts was supported by her immediate predecessor, the Labour MP Alan Johnson.
"I admire Edward in many ways but I fundamentally disagree with him on this," Mr Johnson told Law in Action.
Extradition, he says, should not be a matter for political campaigns - it is either a breach of a suspect's human rights or it is not.
"The best people to decide that, are the people trained in this field who are completely neutral on the matter - judges, not politicians."
Mr Johnson was not in favour of blocking Gary McKinnon's extradition and says politicians were "blundering into" areas they should not go near.
There are strong arguments on both sides of this dispute. On the one hand, the rule of law should not depend on support in an opinion poll.
On the other, governments have a duty to protect their citizens and should be politically accountable for any decision to expel them.
In the end, what matters is that there should be some measure of discretion to cope with new or exceptional circumstances - such as the public interest or a suspect's ill-health.
Whether that discretion is given to judges or politicians is less important: the problem with the 2003 Act is that it offers very little discretion to either of them.