The settlement order was approved by three of the C.F.T.C.'s five commissioners.
Ultimately, Mr. Bansal received about 35 different documents on 20 occasions, according to the settlement order.
Her lawyer, Clifford Van Syoc, said the settlement order was signed Tuesday by Judge Joseph Irenas in United States District Court in Camden.
In both cases, the company dropped the claim and signed a settlement order agreeing to stick with the facts in the future.
The agency has no legal authority to assess fines, although it can bring a civil suit for violations of its settlement order.
The requirement, the trade commission said in the statement, "will give Dannon clearer guidance going forward and help ensure that it complies with the settlement order".
In any case, the attorney has resigned, and Carl J. Barbier, the federal judge who is overseeing the settlement, ordered an investigation, which is continuing.
So it was understandable, perhaps, that there was no celebration after today's settlement order, no high-fives or elated grins.
The agreement expands on a settlement order that Kellogg agreed to last July over similar claims that another cereal, Frosted Mini-Wheats, was "clinically shown to improve kids' attentiveness by nearly 20 percent".
A conference before the judge, Magistrate Judge Cheryl L. Pollak of United States District Court in Brooklyn, is scheduled for Wednesday, and several lawyers involved said they hoped a settlement order would be signed then.
