How complete is the classification of W-symmetries?

In 2D conformal quantum eld theory, we continue a systematic study of W-algebras with two and three generators and their highest weight representations focussing mainly on rational models. We review the known facts about rational models ofW(2; )-algebras. Our new rational models of W-algebras with two generators all belong to one of the known series. The majority of Walgebras with three generators {including the new ones constructed in this letter{ can be explained as subalgebras or truncations of Casimir algebras. Nonetheless, for one solution ofW(2; 4; 6) we reveal some features that do not t into the pattern of Casimir algebras or orbifolds thereof. This shows that there are moreW-algebras than those predicted from Casimir algebras (or Toda eld theories). However, most of the known rational conformal eld theories belong to the minimal series of some Casimir algebra.