The federal judge overseeing the perjury trial of Roger Clemens called in more potential jurors Tuesday morning in his effort to select a final panel of 12 men and women to hear evidence in the case.

Through Monday evening, U.S. District Judge Reggie B. Walton had qualified 35 to be part of a pool of 36 prospective jurors from which the final 12-member panel would be drawn.

But prosecutors and defense lawyers agreed Tuesday afternoon that two of the 35 — one who had been caught sleeping during the selection process — should be struck.

U.S. District Judge B. Walton excused the drowsy one, but he reserved judgment on the other. He then said he would spend the afternoon selecting enough people to fill out the 36-person pool.

The selection process is expected to conclude Tuesday afternoon. Opening statements are scheduled for tomorrow.

During a brief hearing Tuesday morning, defense lawyers signaled they will argue before the jury that Congress’ investigation and hearings were not a “due and proper”uses of its authority, as alleged in the indictment. Defense lawyers are also expected to raise questions about whether Clemens’ statements to a House committee were “material” to any Congressional function or later action.

Legal experts have said that they expect the attorneys to attack the indictment on the grounds that Congress took no official action — other than referring the matter to prosecutors — in the wake of Clemens’ testimony. Therefore, the argument would go, the charges were not “material” to Congress’ work.

Charged with perjury, making false statements and obstruction of Congress, Clemens is accused of lying to a House committee in 2008 when he testified that he had never taken performance-enhancing drugs during his playing days.

The 11-time All Star’s former trainer, Brian McNamee, also testified before the committee that he had actually injected Clemens with steroids and Human Growth Hormone with the pitcher’s knowledge.

Before breaking for lunch, Walton said he was irked that relatives of Clemens had taken to the blogosphere to attack witnesses and others tied to the case. He was apparently referring to a New York Daily News story that pointed out that Clemens’ sister had attacked McNamee on Twitter.

The judge has issued a gag order such that lawyers and witnesses are not permitted to discuss the case with the media. But his order does not apply to relatives of Clemens — unless the former pitcher or his lawyers have directed his family members to attack witnesses.

The “most disturbing” tweets concerned attacks on the father of Andy Pettitte, a former pitcher who is expected to testify at trial, Walton said.

Rusty Hardin, Clemens’ attorney, said he would look into the matter.