This paper presents a case study analyzing a set of software engineering elicitation techniques. The aim of the case study is to demonstrate that completeness and preciseness are two criteria to be incorporated into the set of existing parameters used to classify and select which elicitation technique to apply depending on the project context variables. Completeness refers to how well each elicitation technique elicits domain, task and strategic requirements, and preciseness refers to how many requirements a software engineer is able to elicit using each technique. Based on the results, we can state that completeness and preciseness perform differently for each analyzed technique. Therefore, these two criteria are necessary in order to improve elicitation technique selection. Also, the techniques used in this case study have been ranked according to the above-mentioned criteria, that is, which technique included in this study, is best suited for which requirements layer and which technique can be expected to elicit most requirements during the knowledge externalization phase.