For an incomplete 2 X 2 X 2 contingency table with one missing cell, Fienberg (1972) and Bishop, Fienberg and Holland (1975, pp.237-246) applied four kinds of quasi-independence (QI) models, and gave the estimate of the total population size N under each model. This paper proposes four kinds of new models which have the structure of QI and conditional symmetry, and gives the estimate of N and its asymptotic variance under each new model. Also this paper gives the theorem that when the new model is correct, the asymptotic variance of estimate of N obtained under the new model is less than or equal to it obtained under the corresponding QI model. An example is given. The proposed models derive the more efficient estimate of N and may be more useful than the QI models for inferring N in several incomplete tables.