In a study designed to explore principals' problem-solving strategies, 11 highly effective elementary school principals were compared with 11 moderately effective principals from the same three districts. The principals' effectiveness was determined by central office administrators and by application of the "Principal Profile," a measure of principal effectiveness. The first part of the study, reported in this paper, involved giving these principals a problem-sorting task and subsequently interviewing them. There were marked differences between the two groups in how they classified and managed the problems in their schools, in the strategies they used to solve problems, and in their perceptions regarding the influences of various factors on their problem-solving. The factors considered included administrative experience, personal values and beliefs, school system context, and attitudes. A three-page list of references concludes the document. (PGD)