Conitzer and Sandholm (LOFT-04) constructed an example where a mechanism does better than the revelation principle would allow–if the agent behaves irrationally in any way. We study how generally this phenomenon can be capitalized on, by proving several possibility/impossibility results. Finally, we show that Google's keyword auction (GSP)–a mistake in the sense that it is not incentive compatible–is fortunate in that it has this property (under the usual natural strategy restrictions).