family members - Kaddish yatom: what if a parent really *is* wicked?

I understand that a soul may be judged for a full 12 months after death but that we (generally) only say kaddish yatom for a parent for 11 months because the longest period is for the worst sinners and we presume that our parents are not wicked.

But what if they are? What if, chas v'shalom, one has the misfortune of being the child of somebody he understands to be among the worst sinners and thus in need of the full 12 months? Should he say say kaddish for the full 12 months (to continue to provide benefit to the soul), or should he say it for only 11 months to avoid calling attention to the deceased's wickedness? Does it depend on how public the wickedness is -- maybe if "everybody knows" you go for the full year but if it's more private you don't?

I'd like to clarify that this question is asked out of intellectual curiosity and not out of need. B"H my parents are (a) still alive and (b) definitely not wicked.