The United States v. DiFrancesco case in 1980 revolved around the interpretation of the Double Jeopardy Clause, which prevents a person from being tried twice for the same crime. The defendant, Anthony DiFrancesco, was part of an organized crime family and had been convicted under a federal statute that allowed for increased sentences on appeal by prosecutors. After his initial sentencing, the government appealed to increase his sentence as permitted by this law. However, DiFrancesco argued that this constituted double jeopardy. The Supreme Court ruled against him in a 5-4 decision stating that increasing a sentence did not constitute another trial or punishment but was merely part of one continuous proceeding; thus it didn't violate the Double Jeopardy Clause. This ruling upheld prosecutorial appeals for harsher sentences and clarified how double jeopardy applies to sentencing.

In the dissenting opinion for United States v. DiFrancesco, Justice Brennan argued that the government's ability to appeal a sentence violated the Double Jeopardy Clause of the Fifth Amendment. He stated that this clause not only protects against multiple trials but also against multiple punishments for the same offense. According to him, once a defendant begins serving his sentence, any increase in punishment would constitute double jeopardy. Furthermore, he disagreed with majority’s view that sentencing does not place a defendant in jeopardy because it is merely part of one continuous trial process; instead he believed sentencing should be considered as separate and distinct from trial proceedings where defendants are indeed placed at risk (in "jeopardy"). Therefore allowing an appeal by prosecution after initial sentencing would violate constitutional protections against double jeopardy according to Justice Brennan.