  We compute the Hodge numbers for the quotients of complete intersection
Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the
polynomial deformation method and the counting of invariant K\"ahler classes.
The quotients studied here have been obtained in the automated classification
of V. Braun. Although the computer search found the freely acting groups, the
Hodge numbers of the quotients were not calculated. The freely acting groups,
$G$, that arise in the classification are either $Z_2$ or contain $Z_4$, $Z_2
\times Z_2$, $Z_3$ or $Z_5$ as a subgroup. The Hodge numbers for the quotients
for which the group $G$ contains $Z_3$ or $Z_5$ have been computed previously.
This paper deals with the remaining cases, for which $G \supseteq Z_4$ or
$G\supseteq Z_2 \times Z_2$. We also compute the Hodge numbers for 99 of the
166 CICY's which have $Z_2$ quotients.
