The trend of open data has spread widely in the government nowadays. The motivation to create transparency, accountability, stimulate citizen engagement and business innovation are drivers to open data. Nevertheless, governments are all too often reluctant to open their data as there might be risks like privacy violating and the opening of inaccurate data. The goal of the research presented in this paper is to develop a model for decision-making support for opening data by weighing potential risks and benefits using Bayesian belief networks. The outcomes can be used to mitigate the risks and still gain benefits of opening data by taking actions like the removing privacy-sensitive data from dataset. After the taking of actions the process can start over again and the risks and benefits can be weighed again. The iteration can continue till the resulting dataset can be opened. This research uses health patient stories dataset as an illustration of the iterative process. This shows how the decision-making support can help to open more data by decomposing datasets.