Final Fantasy VI/Gau's sidequest
This sidequest requires no leveling up.
 Part I, Getting Gau in your Party
Simply enter the Veldt with three or fewer members. After fighting Gau will show up and join your party, just as if he had previously "leaped" and was re-joining your group. Just for reference the Veldt is now near the upper right portion of the map, and to the southwest of the weird triangle island where the zone-eaters live. You'll recognize it from the music, the fact that you don't earn any experience there, and that you encounter monsters from all stages of the game.
 Part II, Gau's Father
This quest requires Sabin and Gau. I would recommend waiting to complete this one until you have all the members of your party as some of them say amusing things during the extra scenes. You get no reward for completing it, just a wonderful feeling of satisfaction. On the island between Narshe and the Veldt, which also features the unusual forest with Tyrannosaurs and Brachosaurs, the best monsters to fight in the game, there's a lone house on the left side of the island. Enter it with Sabin and Gau and you'll go through a sequence of getting Gau ready to meet his father.