The item count method is a way of asking sensitive survey questions which protects the anonymity of the respondents by randomization before the interview. It can be used to estimate the probability of sensitive behaviour and to model how it depends on explanatory variables. We analyse item count survey data on the illegal behaviour of buying stolen goods. The analysis of an item count question is best formulated as an instance of modelling incomplete categorical data. We propose an efficient implementation of the estimation which also provides explicit variance estimates for the parameters. We then suggest specifications for the model for the control items, which is an auxiliary but unavoidable part of the analysis of item count data. These considerations and the results of our analysis of criminal behaviour highlight the fact that careful design of the questions is crucial for the success of the item count method.