Some Guard members had been thinking of attending Hammadi's trial, which was scheduled for Tuesday in Kentucky.
The Associated Press, which covered a hearing for Hammadi on Tuesday in Louisville, quoted Justice Department attorney Larry Schneider telling a judge publicly that the government had "definitive proof" that Hammadi was involved in insurgent attacks.
"He was either part of al-Qaeda in Iraq or a group affiliated with al-Qaeda in Iraq," Schneider said.
The government, as in most terrorism cases, has been very tight-lipped about its evidence against Hammadi and Alwan, who also had pleaded guilty.
Alwan, seven years older than Hammadi, was caught on tape by an FBI informant saying he had planted bombs of the same type as in the Alpha attack, in the same period of time, and in the same general location near Beiji, Iraq.
The FBI also matched Alwan's fingerprints to an unexploded bomb made of artillery shells that was found with wires sticking up from the ground near the Alpha Company base on Sept. 1, 2005.
That was three weeks after the attack that killed Pfc. Nathaniel DeTample, 19, of Morrisville; Spec. Gennaro Pellegrini, 31, of Philadelphia; Spec. Francis J. Straub Jr., 24, of Philadelphia; and Spec. John Kulick, 35, of Harleysville.
Hammadi and Alwan were arrested in May 2011 in Bowling Green, Ky., in an FBI weapons sting operation. The Justice Department said they never obtained any of the weapons they had hoped to ship to Iraq.
Hammadi pleaded guilty Tuesday to 10 charges of conspiring to send weapons, cash, and explosives to al-Qaeda in Iraq and two counts of lying to federal immigration agents to get into the United States and stay in the country, the AP reported.
Hammadi, who did not have a plea agreement with prosecutors, faces 25 years to life in federal prison plus millions of dollars in fines when he is sentenced Dec. 5, the AP said.
Alwan is scheduled for sentencing Oct. 3.
Several Alpha veterans have said they may attend at least one of the sentencings.
The Justice Department, while not saying whether either man could be linked to the Alpha killings, included a few Alpha veterans on a victims-notification list in the case.
Sgt. First Class Anthony Kelly, a lawyer and Alpha Company veteran, said it appeared that any evidence linking Hammadi or Alwan to the Alpha attacks would have to be circumstantial.
"They'll never tie them to it, but they don't have to," Kelly said. "These guys are going to spend the rest of their lives in jail."
Tony Khouli, a former Alpha sergeant, said he took comfort in knowing that the FBI and Justice Department had put away two men involved in attacks on U.S. troops - any U.S. troops.
"It doesn't have to be connected to Alpha Company," he said. "It's a good thing they got them."
Contact Tom Infield at 610-313-8205 or firstname.lastname@example.org.