In US Law, you can make an "affirmative defense" [0] if you discover that you possess a small amount of child porn, and either immediately destroy it or immediately turn it over to law enforcement [1]. By doing so, you demonstrate that you did not intend to procure or possess said material, and are therefore not culpable [2].

[0] http://en.wikipedia.org/wiki/Affirmative_defense - admitting to the fact while introducing a factor which justifies it

[1] for example, http://www.law.cornell.edu/uscode/text/18/2252A section (d)

[2] I am not a lawyer. This is not legal advice.