Every Rival card has a "Removal" set of icons. Sometimes this is a pair of book colors, and sometimes it is a colorless book.

For each Little Project card you complete on your turn (but not your Player card personal goal), check its book colors. If it specifically mentions one or more colors, remove all cards that share that color from the Rival queue and shuffle them back into Penelope's deck. This makes future Rival cards less powerful, AND keeps you from running out of Rival cards. Projects focused on colorless books remove colorless Rival cards.

You take the Admire action and accomplish two projects. The first removes all colorless Rival cards. The second removes the Rival card showing a Blue removal icon. Shuffle all removed Rival cards back into the Rival deck.

For each Major Accomplishment you achieve, you may choose a color or colorless and remove all Rival cards matching your choice from the queue. Then, shuffle the removed cards back into the Rival deck.