Some public organisations, despite being committed to attain the ideals of Open Data, struggle to meet the Open Data requirements fully. Often this is the case when their data are of low quality, have (potentially) sensitive information, or have non-interoperable format and semantics. These restrictions, for example, apply quite often to the datasets of justice domain. In practice, nevertheless, many of such public organisations do share their data in a way that partially satisfies the Open Data Requirements in order to be, e.g., transparent. To acknowledge such data opening initiatives, we advocate and describe a method to assess the degree of data openness, as a first step for recognizing such so-called Semi-Open Data initiatives. The proposed method relies on a multi-dimensional method to quantify these initiatives in terms of their adherence, i.e., distance, to the Open Data requirements. We carry out eight case studies and present the results in a way that it shows how to construct and fine-tune the parameters of the proposed method incrementally in a sense making way (i.e., based on consensus among stakeholders involved in a given domain). We report on the feasibility and applicability of the proposed model in practice and the encountered challenges.