Discreet(Adj)= careful and prudent in one's speech or actions, especially in order to keep something confidential or to avoid embarrassment. It is opposite to the word 'Careless'

Antonym: Undiscerning, Reckless, Careless

Synonym: Vigilant, Sagacious, Prudent

Sample sentence:  When he noticed me, he gave me a discreet wink and continued with his speech.