In this paper we provide a structured analysis of US Supreme Court Oral Hearings to enable identification of the relevant issues, factors and facts that can be used to construct a test to resolve a case. Our analysis involves the production of what we term ‘argument component trees’ (ACTs) in which the issues, facts and factors, and the relationship between these, are made explicit. We show how such ACTs can be constructed by identifying the speech acts that are used by the counsel and Justices within their dialogue. We illustrate the application of our analysis by applying it to the oral hearing that took place for the case of Carney v. California, and we relate the majority and minority opinions delivered in that case to our ACTs. The aim of the work is to provide a formal framework that addresses a particular aspect of case-based reasoning: enabling the identification and representation of the components that are used to form a test to resolve a case and guide future behaviour.