In this article, we highlight how, in interdisciplinary, capstone design courses, the most successful teams typically depend heavily on aspects often considered in science and engineering to be "soft skills": flexibility in handling differences, interpersonal strengths in interacting with others, positive attitudes toward collaboration, openness to alternative ideas and approaches, an ability to withhold decisions while various methods and alternatives are considered and weighed We suggest that such elements are often ignored even in the upper-level courses students take, most often due to the real pressures we feel to teach students more technical skill sets associated with our own given disciplines. Yet we argue the importance of explicitly teaching mindsets open to "soft skills" along with or as part of these more specialized skill sets. In this article, we highlight issues that have continued to surface as we have attempted to do just that. In addition, we share some of the less and more successful strategies we have adopted over a five-year collaboration for fostering mindsets that are. often so much more a challenge to teach or to adopt.