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Some discussion regarding "speck of class" in this post:
Hugh: "Speck of class" A "speck of class"? A "speck of dust" but a "touch of class."
Mary: But "touch" wouldn't be right in this context, because there is a silent "even" or "the slightest" before "speck". "Ounce" would be better.
Reconsider the context and speaker: Even an ounce would be too much. But coming from an American speaker, and a cop in mourning, in rage, "millegram" wouldn't do. No, it's got to be speck. (Perhaps it's an unconscious law-enforcement allusion to Richard Speck.)