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1.
To be so into yourself that nothing or nobody else matters.
Some people become so selfpossessed theres no helping them.
by jpg3 October 30, 2011
 
2.
Effortlessly cool(on the surface anyway)and thoughtful, especially in the face of adversity or setbacks; a more ritzy way of describing "composure".
The new waiter Charlie's self-possessed response to the boss's tantrum and finger-pointing quickly established him as one the most powerful employees on the payroll: " The delivery list not having been updated in years is really no one's fault but your own. None of us here were hired to be mindreaders. Sir."
by HairBaron February 03, 2010