Sanity Strengthening

Over the course of a story an insane character actually becomes less insane and more sane as time passes. The opposite of Sanity Slippage. They may start out sane and become insane before becoming sane again. The point of the trope is that they ultimately end up as more or less sane or saner.

Anime and Manga

 * Harry in Outlaw Star. He starts off as an Ax Crazy Stalker with a Crush to Melfina but as the series goes on he becomes more loving and gentle towards her and even makes peace with Gene his enemy before his death.
 * Anemone from Eureka Seven starts off as a violently psychotic Tyke Bomb, but grows much stabler in the presence of her handler/guardian Dominic. Late in the series,.
 * Naruto has Gaara. He starts out Ax Crazy but is now a nice mentally stable guy and is actively trying his best to help Naruto his friend who he once considered his enemy and tried to kill.
 * Also invoked by Al and En from the Makaiju Filler Arc in Sailor Moon, when Al and En start out as Yandere, especially En. In the finale battle Al and En attack the sailor scouts with the intent to kill and seriously hurt them. It all gets better in the end, though, and Al and En leave Earth together and free of their bitterness and insanity.
 * Nina Einstein of Code Geass starts out sane, exhibits Sanity Slippage and and then in the beginning of R2 recovers much of her sanity. Later scenes indicate that her insanity was not so much defeated as it was redirected.

Live Action TV

 * Parker from Leverage fits this trope well. In the pilot, Nate actually says "Parker? She's insane!" And he means it. As the series progresses, she becomes more normal as a result of the family bonding the team experiences as they run jobs together.
 * River Tam on Firefly. Arguably deconstructed - it just means her lucid periods get more frequent, so she's more often aware of her insanity.