Based on corpus data from the Hebrew web corpus HeTenTen, I analyze the discourse argumentative functions of constructions associated with superlative minimum modifiers (e. g. at least). I adopt Kay’s (1992. At least. In Adrienne Lehrer & Eva Feder Kittay (eds.), Frames, fields, and contrasts: New essays in semantic and lexical organization, 309–331. Hillsdale, NJ: Erlbaum) distinction between three such sub-constructions: Scalar, Rhetorical and Evaluative, but I offer further distinctions within these constructions. Most importantly, despite the differences between them, I argue that all three constructions are used to construct non-optimal, yet sufficient arguments.