NEW YORK — Dexter Morgan’s life seemed well-ordered at first glance, including the serial killer thing. That turned out to be unsustainable.

As “Dexter” reaches its finale, to air on Showtime Sunday at 9 p.m. Eastern, the character portrayed by actor Michael C. Hall is no longer strictly ruled by the code set down by his adoptive father upon noticing his son craved killing. Dexter was told only to murder people who are proven killers themselves and likely to kill again, and to thoroughly cover his tracks. The narrative device made it possible for viewers to tolerate, even like, someone who did reprehensible things.