In many transition countries, including Ukraine, decreases in population and fertility have led to substantial falls in the number of school-aged children. As a consequence, these countries now have school networks that consist of many small schools, leading many countries to consider reorganizing their networks by closing smaller schools and reallocating students. Using a rich data-set of almost the entire population of Ukrainian secondary schools, we estimate the effect of school size and class size on the performance of secondary schools on Ukraine's External Independent Test. We find that larger schools tend to have somewhat better performance, both in terms of test scores and in terms of test participation. The size of this effect is relatively small, however, especially in rural areas for which the estimates are likely to be less biased. Class size is found to be insignificant in most specifications and, if significant, of negligible size. The importance of this finding for the 'rationalization' of the large school networks in Eastern Europe is discussed.