Disclosure risk occurs when there is a high probability that an intruder can identify an individual in released sample microdata and confidential information may be revealed. For some social surveys, the population from which the sample is drawn is generally not known or only partially known through marginal distributions. The identification is made possible through the use of a key, which is a combination of indirectly identifying variables, such as age, sex, and place of residence. Disclosure risk measures are based on the notion of population uniqueness in the key. In order to quantify the disclosure risk, probabilistic models are defined based on distributional assumptions about the population counts according to the observed sample counts. The parameters for the distribution are estimated through log-linear models. The model selection criteria is based on a ‘minimum error’ test using a forward search algorithm. The methods are expanded to cover the case of complex survey designs and misclassification on the key variables, either arising from the survey process or as a result of perturbative disclosure control techniques that may have been applied to the data. Variance and confidence intervals of estimated disclosure risk measures are also addressed. The methods are demonstrated on real data drawn from extracts of the 2001 UK Census. Possible extensions to the probabilistic modeling are presented based on a local polynomial regression smoothing technique in neighborhoods of the cells of the key.