Both were called to give evidence of the first day of the committee hearing, which will also hear from a number of other witnesses.
Mr Laidlaw, who is a non-executive director of the DfT, is due to give evidence to the House of Commons transport committee next week.
Mr Levy's widow, Tina, was forced to give evidence a total of five times.
The very fact of requiring ministers and their officials to give evidence has often resulted in changes of policy.
He asked for trial dates to be postponed so that experts could be available to give evidence about the use of police batons.
And it doesn't mean an indictment is inevitable, but now it means that people will be required to give evidence or face contempt of court charges or will have to evoke their Fifth Amendment rights.
The transport secretary said the investigation by Mr Laidlaw - who will give evidence to the House of Commons Transport Select Committee on 18 December - found department officials "wrongly calculated the amount of risk capital bidders would have to offer to guarantee their franchise proposals".
So, federal rules of evidence give a lot of leeway to prosecutors in this area.
Liverpool chose not to give evidence but in court excerpts of his diary were read out.
Mr McDonnell, who is an MP on the Northern Ireland Affairs Committee, switched roles to give the committee evidence on behalf of his party.
Esack, of Rosewood Drive, declined to give evidence at his trial but had told police he had intended to kill himself in front of her after being badly affected by her beginning a new relationship after the couple had split up.
Those who come forward can limit their engagement with the inquiry to just the forum, or decide to progress and give evidence to the inquiry's lawyers in the public phase of the investigation.
Ms Lees, who works with people with learning difficulties in East Sussex, has travelled thousands of miles to give evidence.
Ofqual is expected to give evidence on Thursday, the final day of the hearing.
Medics involved in treating Mrs Halappanavar will be called to give evidence along with experts including former master of the National Maternity Hospital Dr Peter Boylan.
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Mr Jamil, who said he had been known as K-dog since the age of 17, was the first of the defendants to give evidence in the trial.
"I've been taking phone calls from social workers and other health care professionals who say it would be a routine part of their work to give evidence in very complex court cases, " she said.
Connecting the advice doctors give to the scientific evidence is the point of a new commentary on obesity appearing this week in the electronic edition of the respected New England Journal of Medicine (NEJM), Myths, Presumptions, and Facts About Obesity.
Professor David Heald of the University of Aberdeen was next to give evidence on the spending review.
About 76 witnesses will be called to give evidence, including the serving and former head of the Prison Service.
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Ms Kelly, who was the first witness to give evidence in the trial, told the jury of the moments just before her son's death on 25 May.
Among witnesses invited to give evidence are Lady Warnock herself and two parents of children with special needs who have been vocal critics of current policy: Julie Maynard and Maria Hutchings.
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In court on Monday, Malcolm Gibney, prosecuting on behalf of Trading Standards, asked Henry Mears if he was he going to call any of the market traders to give evidence who he alleges Mr Cooper turned away.
As she had not yet had an opportunity to assess the applications, chair of the committee Rhodri Glyn Thomas AM invited the minister to give further evidence to the committee in the spring.
Even if, unlikely as it seems at present, Mr Hussein agrees to give carte blanche to Unmovic to scour Iraq for evidence of nuclear, biological and chemical weapons, that may not be enough to convince everyone that the country is no longer a threat.
Members of the emergency services are also to give evidence along with the NI Heath and Safety Executive.
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The prime minister said he would "answer all the questions" asked of him if he was called to give evidence.
Tracy White, who is due to give evidence to the tribunal on Friday, faces five charges of falsifying records and failings over patient care.
"They have to prove on the balance of probabilities ... what happened to them and that will be forensically tested, there will be independent psychiatric reports for all of them and they will have to give evidence and satisfy the court that they're telling the truth, " she said.
Independent retailers had complained that oil companies and supermarkets had been using their scale to give themselves an unfair advantage, but the regulator found no evidence of this.
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