Open Learner Models (OLM) show the learner model to users to assist their self-regulated learning by, for example, helping prompt reflection, facilitating planning and supporting navigation. OLMs can show different levels of detail of the underlying learner model, and can also structure the information differently. As a result, a trade-off may exist between the potential for better support for learning and the complexity of the information shown. This paper investigates students' perceptions about whether offering more and richer information in an OLM will result in more effective support for their self-regulated learning. In a first study, questionnaire responses relating to designs for six visualisations of varying complexity led to the implementation of three variations on one of the designs. A second controlled study involved students interacting with these variations. The study revealed that the most useful variation for searching for suitable learning material was a visualisation combining a basic coloured grid, an extended bar chart-like visualisation indicating related concepts, and a learning gauge.