Even when Vallance started working with Bryan Adams, he remained active (as a songwriter) with Prism, and in the summer of 1981, Vallance and Adams wrote "Don't Let Him Know" for Prism. Vallance has subsequently stated that the song was influenced by "Bette Davis Eyes," and I think that you can hear that, especially in the drums. In any event, "Don't Let Him Know" would go on to be Prism's only top 40 hit in the U.S., making them an official one-hit wonder (although, to be fair, they had three other songs that broke the U.S. top #100).
I don't think that an official video was ever made for the song (if any readers know of one, please let me know in the comments). As a result, I have gone with a clip from Solid Gold, although, sadly, the Solid Gold Dancers do not make an appearance. Prism broke up in 1982, although the band later re-formed and continues to play to this day.
Coll trivia fact: Bruce Fairbairn would go on to become a hugely successful record producer for Krokus, Loverboy, Aerosmith, Bon Jovi, and AC/DC among others until his untimely passing in 1999.