The paper aims to weaken a widespread argument against indexical contextualism regarding matters of personal taste. According to indexical contextualism, an utterance of "T is tasty" (where T is an object of taste) expresses the proposition that T is tasty for J (where J is a judge). This argument suggests that indexical contextualism cannot do justice to our disagreement intuitions regarding typical disputes about personal taste because it has to treat conversations in which one speaker utters "T is tasty" and another responds with "T is not tasty" (referred to as 'judge-non-specific conversations' in this paper) as being on a par with conversations in which one speaker utters "T is tasty to me" and another responds with "T is not tasty to me" (referred to as 'judge-specific conversations'). The argument has it that judge-specific conversations, unlike judge-non--specific conversations, do not contain disagreement between speakers. To defend indexical contextualism, some philosophers have proposed accounts (here referred to as 'dual-proposition theories') according to which utterances of "T is tasty" are used to communicate both the above kinds of semantically expressed proposition and some other kinds of proposition (like superiority propositions or metalinguistic propositions) that could be used to explain disagreements about taste. The paper defends two claims: First, it is argued that judge-specific conversations, or at least some of them, do contain disagreement between speakers, contrary to what the anti-indexical-contextualist argument supposes. Second, it is argued that dual-proposition indexical-contextualist theories fail to explain judge-specific conversations that are intuitively interpreted as containing disagreement.