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International comparisons of poverty are traditionally based on the head count and poverty gap ratios. Using the Luxembourg Income Study (LIS) microdata, the present paper extends the comparative measurement of poverty to utilize alternative measures which take account not only of the "width" and the "depth" of poverty but of the income distribution among the poor as well (Sen, 1976; Kakwani, 1980; Foster, 1984). It is found that given any poverty line these three measures yield a completely different ranking from the traditional head count and poverty gap ratios. Also, whereas the traditional two measures lead to contradicting rankings, the alternative measures register (with only few exceptions) the same ranking. In spite of the fact that the ranking of countries by all the poverty measures examined is not preserved under alternative poverty lines, considerably fewer rerankings occur with respect to the measures which incorporate all three poverty dimensions.