OMAHA, Neb. — The Nebraska Supreme Court on Friday rejected a death-row inmate’s call for his murder convictions in one of the deadliest bank shootings in U.S. history to be overturned because he said the lawyer defending him was incompetent.

The state’s high court agreed with a lower court that refused Erick Vela’s request to void the convictions.

Vela and two other men were sentenced to death for killing five people at a U.S. Bank branch in Norfolk on Sept. 26, 2002. A fourth man who served as a lookout was sentenced to five consecutive life sentences.

Vela pleaded guilty in June 2003 to five counts of first-degree murder in the killings of bank customer Evonne Tuttle and bank employees Lisa Bryant, Lola Elwood, Jo Mausbach and Sam Sun. Vela was sentenced to death in 2007 for the botched heist at the bank about 90 miles northwest of Omaha.

The high court found no merit to Vela’s claims, including one in which he faulted his attorney for not advising him to plead guilty earlier in the case. Vela asserted he would not have been subject to the death penalty had he pleaded guilty earlier, because Nebraska enacted a revised death penalty law in late 2002 to comply with a U.S. Supreme Court ruling that said juries — not judges — should determine whether a defendant is eligible for the death penalty.

Previous Nebraska Supreme Court rulings in the bank killings case undermined that argument, Justice Lindsey Miller-Lerman wrote.

Those rulings rejected arguments that Nebraska effectively had no valid death penalty before the law was amended in 2002.

Vela’s attorney did not return a message left Friday seeking comment. The Nebraska Attorney General’s Office declined to comment.