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Priggish
Negative Connotation
Priggish has a negative tone, suggesting unnecessary or excessive strictness in moral matters. 
Often Annoying
Using 'priggish' implies that someone's behavior is irritating or annoying due to their self-perceived superiority. 
Not Just Honest
'Priggish' isn't just about honesty; it's about being overly showy in one's morality. 