In this Icon design, I feel that brand recognition is most important. So, I felt that it would be necessary to do the same to the icon as to what the logo looks like. Since you like the look and feel of your current logo. I decided to keep the icon the same as the logo but just shorten it by using the initials instead while emphasizing that it deals with books I incorporated a book in the icon that fits the overall stamp look and feel. So, the icon is still connected to the overall brand while standing out some from the logo with the book to differentiate the two.