Summary. A methodology is developed to estimate comparable international migration flows between a set of countries. International migration flow data may be missing, reported by the sending country, reported by the receiving country or reported by both the sending and the receiving countries. For the last situation, reported counts rarely match owing to differences in definitions and data collection systems. We report counts harmonized by using correction factors estimated from a constrained optimization procedure. Factors are applied to scale data that are known to be of a reliable standard, creating an incomplete migration flow table of harmonized values. Cells for which no reliable reported flows exist are then estimated from a negative binomial regression model fitted by using an expectation–maximization (EM) type of algorithm. Covariate information for this model is drawn from international migration theory. Finally, measures of precision for all missing cell estimates are derived by using the supplemented EM algorithm. Recent data on international migration between countries in Europe are used to illustrate the methodology. The results represent a complete table of comparable flows which can be used by regional policy makers and social scientists to understand population behaviour and change better.