Computer-supported discursive learning (CSDL) systems for the support of asynchronous discursive learning need to fulfill specific socio-technical conditions. To understand these conditions, we employed design experiments combining aspects of communication theory, empirical findings, and continuous improvement of the investigated prototypes. Our theoretical perspective starts with a context-oriented model of communication which is--as a result of the experiments--extended by including the role of a third-party such as a facilitator. The theory-driven initial design requirements lead to the CSCL-prototype, KOLUMBUS, emphasizing the role of annotations. In KOLUMBUS, annotations can be immediately embedded in their context of learning material. Practical experience with the prototype in five cases reveals possibilities for implementing improvements and observing their impact. On this basis, we provide guidelines for the design of CSDL systems that focus on the support of asynchronous discursive learning.