Research on CALL has witnessed a renewed interest in task design as evidenced by the number of peer-reviewed publications and conference presentations that link task design to technology. This interest has also translated into a surge of studies addressing task design with a focus on output-based tasks such as L2 writing and L2 speaking. However, as in other areas of research in English Language Teaching, task design in L2 listening remains under-researched. The qualitative case study reported here is the first stage of a three-stage research study that aims to put forward a theoretically-and-an-empirically-based framework for the design of tasks in computer-based L2 listening environments. Accordingly, we elicited the personal goals of listeners of English as a foreign language with a view to identifying characteristics of computer-based L2 listening tasks. The participants are 68 high-school students from public and semi-public schools in Chile. Using established techniques for data collection from an Educational Engineering perspective (Colpaert, 2010) the data comes from an entry-questionnaire and three focus group sessions where participating students explored, reflected, shared their personal goals and their expectations about tasks for computer-based L2 listening environments. The verbal data were transcribed, analyzed and emerging characteristics identified. Characteristics of computer-based listening tasks are grouped and presented as three components: input, task structure, and levels of support and guidance. Results are discussed along with integrated data.