It is of fundamental importance that school superintendents engage in the vertical dimension of school governance within the national education system, but have these vertical structures been given too much attention, to the detriment of horizontal organisational structures? The chapter is based on material collected at a workshop where 52 Swedish school superintendents were in attendance. A conclusion is that superintendents are faced by fields of tension in both the vertical and the horizontal dimension of organisational structures. Three types of tensions were identified in relation to: (i) administrative questions, (ii) the students’ experiences, and (iii) organisational units. It is furthermore suggested that the superintendents see themselves to be the ‘victims’ of these tensions. We introduce the concept of ‘unmanaged spaces’ to address the need for competence to act in a constructive and responsible manner to diffuse the above-mentioned tensions. Our hypothesis is that far too narrow a focus on line management and governance documents has resulted in superintendents who are unable to properly manage collaboration in complex situations. This state of affairs is somewhat worrying in a government agency that is expected to be essential to democracy and should pursue ways of working where coordination and collaboration are fundamental.