Although central office supervisors are emerging as critical linchpins of school improvement efforts, research is quite limited in this area. This study differs from previous efforts by focusing on the administrator's real world and identifying the subjective role conceptions and statements shared by four outstanding central office supervisors. It provides data based on shared meanings (held in common despite variances in social context) as determined by qualitative analysis of open-ended, in-depth interviews. The study ignores a priori constructs held by the researcher or authorities in the field. Findings suggest that effective supervisors are highly flexible and able to cope successfully with the fragmentation, ambiguity, and invisibility characterizing their role. These role aspects, far from being problematic, ensure access to various levels of information and enhance the supervisor's ability to respond well to individual differences, the needs of a diversified staff, and changes in leadership and programs. The capacity to respond appropriately characterizes principals possessing more complex cognitive structures. Preparation programs should provide specific training in solving complex problems and in metacognition. Included are 2 tables and 119 references. (MLH)