Biblically, it would have been enough to mentally give up ownership of the Leaven: Pesachim 4b
From the time when the Rabbinic Prohibition sets in, the Leaven no longer belongs to its owner, except for liability for the prohibition against owning the Leaven: Pesachim 6b-7a
Annulling Leaven instead of destroying it, if one does not have enough time to do destroying it and slaughter the Pesach Offering or circumcise his son or eat his meal celebrating kiddushin: Pesachim 49a
Annulling Leaven instead of destroying it if one is involved in an action of saving lives or property from danger: Pesachim 49a
Annulling Leaven instead of destroying it if one is involved in a voluntary deed involving one's property: Pesachim 49a
Marriage of a woman with a gift of Leaven on Pesach, even a substance which is only Leaven Rabbinically, is invalid after the 6th hour of the eve of Pesach: Pesachim 7a, 21b
Doing the annulment at night after Searching for Leaven: Pesachim 6b-7a
Considering Leaven to be under a person's protection if he is guarding the area in which it lies: Pesachim 6b
Ability to annul Leaven found on Pesach itself: Pesachim 6b-7a
Annulment is required even for Leaven buried below 3 hand-breadths in the ground: Pesachim 31b
