We construct several quantum coset W algebras, e.g. sl(2,R)/U(1) and s
l(2,R) + sl(2,R)/sl(2,R), and argue that they are finitely nonfreely g
enerated. Furthermore, we discuss in detail their role as unifying W a
lgebras of Casimir W algebras. We show that it is possible to give cos
et realizations of various types of unifying W algebras; for example,
the diagonal cosets based on the sympletic Lie algebras sp(2n) realize
the unifying W algebras which have previously been introduced as WD(-
n). In addition, minimal models of WD(-n) are studied. The coset reali
zations provide a generalization of level-rank duality of dual coset p
airs. As further examples of finitely nonfreely generated quantum W al
gebras, we discuss orbifolding of W algebras which on the quantum leve
l has different properties than in the classical case. We demonstrate
through some examples that the classical limit - according to Bowcock
and Watts - of these finitely nonfreely generated quantum W algebras p
robably yields infinitely nonfreely generated classical W algebras.