Focusing on the problem of authority, an analysis of the theories of Max Weber, James D. Thompson, and Elliott Jaques forms the basis for this proposal for improved organizational effectiveness in public schools. Basic assumptions are that modern organizations are established and operated under rational principles and subject to rational analysis, that in order to improve an organization's effectiveness administrators must act on its structure, and that in changing this structure administrators modify authority relationships between members. Thus, if fashionable but cosmetic remedies are imposed, schools' deep-seated structural problems are neglected. The organizational structure of schools can be improved by working for greater congruence with a triadic model granting each staff position, except teachers, requisitely rational authority--involving two-way accountability--over subordinates. Practical recommendations drawn from the model include: granting principals more authority; clarifying the limits of authority of intermediate assistants, thereby placing principals and teachers in more direct contact; redefining the role of vice principals as buffering principals and teachers from environmental turbulence; defining accountability relationships more clearly; implementing school-based budgeting; and improving teachers' access to principals and chief executive officers. An alternative theoretical analysis is summarized which implies that principals' main task is to buffer teachers from the disturbances of administrative bureaucracy. (MJL)