In 2D conformal quantum field theory, we continue a systematic study o
f W-algebras with two and three generators and their highest weight re
presentations focussing mainly on rational models. We review the known
facts about rational models of W (2, delta)-algebras, in particular t
hose models that are not related to some generically existing algebra.
However, our new rational models of W-algebras with two generators al
l belong to one of the known series. The majority of W-algebras with t
hree generators - including the new ones constructed in this letter -
can be explained as subalgebras of Casimir algebras. Nonetheless, for
one solution of W (2, 4, 6) we reveal some features that do not fit in
to the pattern of Casimir algebras or orbifolds thereof. This shows th
at even a classification of all Casimir algebras (or Toda field theori
es) will probably fail to classify all rational conformal field theori
es.