The lawyers also argued that death penalty opponents should be allowed to serve on Holmes' jury, and that victims of the shooting shouldn't be permitted to testify when the jury is deciding punishment.
Holmes has pleaded not guilty by reason of insanity to multiple charges of murder and attempted murder in the attack that killed 12 people and injured 70 others in a suburban Denver movie theatre in July 2012. Prosecutors are seeking the death penalty.
The trial is scheduled to start in February.
The defence filed 20 motions last week that were made public Tuesday. Six were challenges to the death penalty, arguing among other things that Colorado executes prisoners so rarely that it falls under the U.S. Constitution's ban on cruel and unusual punishment. The state has executed only one person since 1967.
The defence also said Colorado prosecutors are so inconsistent in whether they seek the death penalty that it has become arbitrary and capricious, again violating the Constitution.
In 10 years, prosecutors have sought the death penalty in only six of Colorado's 64 counties, the defence said.
To support their case, defence lawyers quoted Gov. John Hickenlooper, who granted an indefinite reprieve to death row inmate in May. Hickenlooper cited doubts about the fairness of Colorado's death penalty system and noted inconsistencies from county to county.
Holmes' lawyers began questioning the death penalty even before prosecutors announced in April that they would seek it. They filed other challenges in May and August. Arapahoe County District Court Judge Carlos A. Samour Jr. rejected some but hasn't ruled on others.
In another motion, the defence asked Samour not to automatically disqualify potential jurors because they oppose the death penalty.
Citing social science research, the defence said barring death penalty opponents produces juries that are partial to the prosecution, biased against the defence, and more likely to convict a defendant. That violates Holmes' right to a fair trial, they said.
The defence also said allowing victims to testify during the penalty phase — which would happen only if Holmes were convicted — would overwhelm jurors with emotion and keep them from relying only on facts if they have to decide between execution and life without parole.
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