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Adjective: buttoned-down
  1. [US, informal] Unimaginatively conventional
    "a colourful character in the buttoned-down, dull-grey world of business";
    - button-down, conservative
     
  2. (of clothing, especially shirts) having the collar fastened down with buttons
    "He always wore buttoned-down oxford shirts"

See also: conventional, mainstream, staid, stodgy, stuffy