Statistical modeling of school effectiveness data was originally motivated by the dissatisfaction with the analysis of (school-leaving) examination results that took no account of the background of the students or regarded each school as an isolated unit of analysis. The application of multilevel analysis was generally regarded as a breakthrough, although more recent assessments of how they satisfy the goals of school effectiveness studies, to compare the performances of schools, are much more guarded. This article shows that the association of the school effects with randomness is not necessary, because strength can be borrowed across the analyzed schools even when they are associated with fixed effects. The methods are illustrated on a reanalysis of the data from an early study of school effectiveness. It also addresses the problem of excess zero outcomes by treating them as censored (truncated). (Contains 4 tables and 3 figures.)