Bin Attash, Aziz Ali and al-Hawsawi, eventually entered the high-security Guantanamo courthouse, where lawyers had already started arguments without them.
Ramazi Binalshibh and bin Attash, both Yemeni, Mohammed and Aziz Ali, both Pakistanis, and al-Hawsawi, a Saudi, could receive the death penalty if they are convicted on charges that include murder, conspiracy and terrorism.
Thursday's hearing was concerned with legal motions regarding whether Binalshibh and al-Hawsawi are fit to stand trial.
Navy Commander Suzanne Lachelier, Binalshibh's lawyer, asked the court to permit a defence analyst to check CT scans of her client's brain.
She also said that further tests, including an MRI, could be undertaken to "determine whether any lesions in [Binalshibh’s] brain affect his cognitive functioning".
Binalshibh was diagnosed with a mental disease that resulted in doctors prescribing psychotropic drugs used to treat schizophrenia or bipolar disorder, defence documents showed.
However, a censor in the court stopped Lachelier when she referred to Binalshibh's complaints that he had been deprived of sleep by officials at the prison.
Sleep deprivation has been criticised by human rights groups as an abusive technique used to gain control over suspects during interrogation.
Clayton Trivett, a military prosecutor, said that Binalshibh's allegations of abuse, which also included being subjected to loud noise, could be explained by the fact that he has been diagnosed as delusional.
"The government's position is that it's not happening and it's never been happening," he said.
The pre-trial hearings, which began on Wednesday, are the first to be held at the prison camp since Barack Obama became US president.
Obama has suspended prosecutions pending the outcome of his administration's review of the war crimes tribunals, the first that the US has held since World War Two.