Inspect and adapt is essential to succeed with agile software development. Our objective was to understand the challenges of software process improvement in agile software development teams. We designed a multiple case study consisting of five projects in three software product companies that applied Scrum. We collected data in semi-structured interviews. We found that long-term quality was often in conflict with short-term progress, specialization hinders self-management, process related problems are difficult to solve and there are major organizational barriers to self-management. The main conclusion drawn from this work is that software process improvement challenges in agile software development are the problems of increasing redundancy to create conditions for the team to self-manage, to learn how to learn, and to improving agile software development as a large long-term organizational change project.