At the turn of the millennium, major international organizations (UN, WB, OECD) revolutionized international migration studies by publishing new global bilateral matrices of international migration. These data are now extensively used for descriptive purposes, for estimating flows and to study the determinants and consequences of migration. For the most, they are based on the same methodological principles and use the same data sources. They should give very similar measures of international migration. In this paper, we present a new comparative database, ABIMS (Aggregated Base of International Migrants Stocks), which allows us to compare estimates of all sources. We show significant discrepancies in the measurement of international migrant stocks and propose a method to identify outliers in matrices. A systematic analysis of the available documentation related to the UN and WB databases provides insights to explain discrepancies but does not allow to fully understand them.