U.S. government promises that WikiLeaks founder Julian Assange would not face harsh prison conditions if he is extradited to face American justice are not enough to address concerns about his fragile mental health and high risk of suicide, a lawyer defending him argued Thursday.

Assange’s lawyer, Edward Fitzgerald, said during a two-day hearing at Britain’s High Court that the Australian was too mentally ill to be extradited to the United States to face trial on espionage charges.

Washington is seeking to overturn an earlier ruling by a lower British court that refused a U.S. request to extradite Assange over WikiLeaks’ publication of secret American military documents a decade ago. District Judge Vanessa Baraitser ruled that Assange was likely to kill himself if held under harsh U.S. prison conditions.

On Wednesday, a lawyer for the U.S. government said that American authorities have promised that Assange would not be held before trial in a top-security “Supermax” prison, or subjected to strict isolation conditions. He also said that if convicted, Assange would be allowed to serve his sentence in Australia, his home country.

But Fitzgerald argued that the U.S. assurances were all “caveated, vague, or simply ineffective.” They do not remove the risk of Assange being detained in extreme isolation in the U.S. in the long term, he said, and the risk of Assange killing himself remained substantial if he is extradited.