This report presents attempts to understand more about how six background characteristics (small scale, population sparsity, district isolation within a BOCES (Boards of Cooperative Educational Service), interaction between a change in enrollment and initial scale of the district, rapid changes in full value property wealth over time, and large discrepancies between income and property based measures of ability to pay) affect financing and delivery of educational services. Each characteristic is examined in turn and discussion includes a rationale for expecting each characteristic to make a difference either for taxpayers or students. Two distinct types of burdens are addressed: the first type involves hardships that stem from whatever extra costs certain districts are forced to incur in producing a given level and mix of educational outcomes, and the second type involves instances of the state's inaccurate determination of the school district's ability to pay for educational services. The report concludes with a discussion of policy alternatives considered in response to seven questions, e.g., should the state concern itself with the limited extent to which small districts cooperate for the purpose of providing educational services, and should the state make allowances for the current size of districts when it makes adjustments for declines in pupil enrollment? (BRR)