The Claim: "If we want to reform human rights laws in this country, it isn't the EU we should leave but the ECHR and the jurisdiction of its court."
Reality Check verdict: If the UK wanted to stay in the EU but leave the ECHR, the European Commission would have to decide whether that meant the UK had too little respect for human rights to stay in the Union. Nobody has tried it before and lawyers disagree about what the Commission's conclusion would be.
In a speech on Tuesday, Home Secretary Theresa May proposed that the UK should leave the European Convention on Human Rights but stay in the European Union.
"It wasn't the European Union that delayed for years the extradition of Abu Hamza, almost stopped the deportation of Abu Qatada, and tried to tell Parliament that - however we voted - we could not deprive prisoners of the vote. It was the European Convention on Human Rights," she said.
The first thing to do is distinguish between two courts: the European Court of Justice (ECJ) and the European Court of Human Rights (ECHR).
The ECHR, which was indeed involved in the Abu Qatada case and some (but not all) of the cases about prisoners being allowed to vote, is not part of the EU.
Its job is to uphold the European Convention on Human Rights, which was drawn up after World War Two, partly thanks to Winston Churchill. The Convention is incorporated into UK law by the Human Rights Act (HRA).
The other court is the ECJ, which is an EU institution. Its job is to uphold EU law, including the right of free movement, and so it can rule on deportations.
It has also made rulings on prisoners' voting rights and may be involved if the UK tried to deport or bar entry to criminals who are from the EU or related to EU citizens, for example.
If the UK were to leave the EU, it would no longer be bound by rulings from the ECJ, but it would still be bound by the ECHR, unless it decided to leave that as well.
But could the country, as Theresa May suggests, leave the ECHR and abolish the Human Rights Act, but stay in the EU?
That's tricky. There's disagreement between lawyers as to whether adherence to the ECHR is a condition of EU membership, as this House of Commons Library research paper makes clear.
The European Commission has said that it uses being a signatory of the Convention as a way for countries to demonstrate that they have the respect for human rights required for membership.
"Any member state deciding to withdraw from the Convention and therefore no longer bound to comply with it or to respect its enforcement procedures could, in certain circumstances, raise concern as regards the effective protection of fundamental rights by its authorities," the Commission said in 2007.
Under such circumstances, the Commission would have to decide whether whatever replacement the UK decided to enact in place of the Convention demonstrated sufficient respect for human rights to allow for continued membership.