Composite indices are increasingly recognized as a useful tool to measure socio-economic phenomena such as quality of life, competitiveness, development, and poverty. Considerable attention has been devoted in recent years to the methodological issues associated with composite index construction, particularly non-compensability and comparability of the data over time. In this paper, we compare two non-compensatory composite indices for measuring multidimensional phenomena and monitoring their changes over time: the Adjusted Mazziotta-Pareto Index (AMPI) and the Mean-Min Function (MMF). The AMPI is a non-linear composite index that rewards the units with balanced values of the individual indicators. The MMF is a two-parameter function that allows compensability among dimensions with a cost that increases with unbalance and can be seen as an intermediate case between a compensatory and a full non-compensatory index. An application to a set of individual indicators of development in the Italian regions is also presented.