Hayate no Gotoku! Character Cover CD is a special character CD in which Kenjiro Hata picked several songs for each character. All songs come from the many hit titles, mostly from anime. It was first released on March 6, 2008 by Geneon. The song "A Cruel Angel's Thesis" was used as an Insert song in Hayate no Gotoku!! 2nd SeasonEpisode 12, following the Hayate no Gotoku! MangaChapter 95.
The song Niji iro no Sneaker is the song Nagi sang in her karaoke duel against Ayumu in Chapter 48, but in the anime adaption from Hayate no Gotoku! Season 1, she sang her character song, Dame! instead. That's why Niji iro no Sneaker doesn't count as an insert song.