We discuss in some detail three new cluster variation approximations w
e used in a previous paper in connection with Pade approximants to inv
estigate critical behaviour of classical spin models on various lattic
es. The approximations are applied to the Ising model on the simple cu
bic, face centered cubic, and semi-infinite simple cubic lattices. The
natural iteration equations and estimates for the critical temperatur
es and for the range of validity of the approximations are given.