We theorize a two-mind model of design thinking. Mind 1 is about logical design reasoning, and Mind 2 is about the reflection on our reasoning and judgments. The problem solving ability of Mind 1 has often been emphasized in software engineering. The reflective Mind 2, however, has not received much attention. In this study, we want to find out if Mind 2, or reflection, can improve design discourse, a prerequisite of design quality. We conducted multiple case studies with 12 student groups, divided into test groups and control groups. We provided external reflections to the test groups. No reflections were given to the control groups. We analyzed the quality of the design discourse in both groups. We found that reflection (Mind 2) improves the quality of design discourse (Mind 1) under certain preconditions. The results highlight the significance of reflection as a mean to improve the quality of design discourse. We conclude that software designers need both Mind 1 and Mind 2 to obtain a higher quality design discourse, as a foundation for a good design.