The antonyms for the word "more undiscriminating" are "discriminating," "selective," and "judicious." Discriminating refers to an individual's ability to distinguish between different things and make choices based on their value or quality. Selective denotes the careful choice between a large number of different options, based on the underlying factors that influence the decision-making process. Judicious refers to a wise and prudent approach, using good sense and sound reasoning to ensure desirable outcomes. These antonyms emphasize the importance of careful analysis, thoughtful consideration, and critical thinking when making judgments or decisions, rather than relying on haphazard or arbitrary methods.