This paper proposes a new methodology for multidimensional poverty measurement consisting of: (i) an identification method ?k that extends the traditional intersection and union approaches, and (ii) a class of poverty measures M? that satisfies a range of desirable properties including decomposability. Our identification step makes use of two forms of cutoffs: first, a cutoff within each dimension to determine whether a person is deprived in that dimension; second, a cutoff across dimensions that identifies the poor by counting the number of dimensions in which a person is deprived. The aggregation step employs the FGT measures, appropriately adjusted to account for multidimensionality. The identification method is particularly well suited for use with ordinal data, as is the first of our measures, the adjusted headcount ratio. We provide illustrative examples using data from Indonesia and the US to show how our methodology might be used in practice.