Antonyms of adj bigmouthed

1 sense of bigmouthed

Sense 1
bigmouthed, blabbermouthed, blabby, talkative -- (unwisely talking too much)

INDIRECT (VIA indiscreet) -> discreet -- (marked by prudence or modesty and wise self-restraint; "his trusted discreet aide"; "a discreet, finely wrought gold necklace")

Similarity of adj bigmouthed

1 sense of bigmouthed

Sense 1
bigmouthed, blabbermouthed, blabby, talkative -- (unwisely talking too much)
       => indiscreet (vs. discreet) -- (lacking discretion; injudicious; "her behavior was indiscreet at the very best")