The case of Brady v. United States involved a petitioner who changed his plea to guilty for kidnapping upon learning that his codefendant would testify against him. He later sought relief, claiming that his plea was not voluntary and that the trial judge did not comply with Rule 11 of the Federal Rules of Criminal Procedure. The Supreme Court affirmed the lower court's decision, stating that the petitioner's plea was voluntary and met the requirements for a valid guilty plea. The Court declined to rule that a guilty plea is invalid under the Fifth Amendment if motivated by the defendant's desire for a lesser penalty. The decision in United States v. Jackson did not create a new standard for judging the validity of guilty pleas. A guilty plea must be voluntary, and the defendant must be aware of the relevant circumstances and likely consequences.

Guilty pleas are allowed and can be beneficial for both the defendant and the State. Confessions must be given freely and voluntarily without any threats, violence, promises, or improper influence. Brady's guilty plea was voluntary, informed, and intelligently made with competent counsel. He cannot withdraw his plea just because he misjudged the strength of the case against him or the potential penalties. The court affirms the decision.