Information about how school principals operate pertains mainly to the actions of principals. However, the kinds of knowledge that the principalship demands have not been isolated as clearly, more often than not being conflated with actions. As principals' duties become more complex, it becomes more important to ground specific practices in robust knowledge of relevant theoretical principles. One aspect of the principal's job where this is particularly germane is the resolution of unfamiliar, complex, unstructured challenges. This paper presents findings from research into how principals think when dealing with problematic situations, in particular the types of knowledge they use. Four broad categories of knowledge were identified and, within those, twelve specific types. The research lends credence to the oral report or think-aloud method for making thinking processes available for analysis, and the findings indicate how the content of preparation programs may be adjusted to better qualify principals for the contemporary demands of their work. A prime recommendation is the inclusion of opportunities for the development of tacit knowledge. (Contains 1 figure and 5 tables.)