Button-down and Unflappable

Button-down adjective - Tending to favor established ideas, conditions, or institutions.

Unflappable and button-down are semantically related. In some cases you can use "Unflappable" instead an adjective phrase "Button-down".

Unflappable adjective - Not easily panicked or upset.

Button-down and unflappable are semantically related. Sometimes you can replace phrase "Button-down" with "Unflappable", this terms are similar.