I propose a method for estimating migration flows between all pairs of countries, including breakdowns by place of birth. My estimator is a pseudo-Bayes estimator which smooths a set of state-of-the-art estimates of migration flows towards a simpler estimate which contains fewer structural zeroes. The smoothing process provides a natural way to bypass the state-of-the-art estimator's unrealistic assumption that the number of global migrants is as small as possible. I produce estimates of global migration flows at five-year intervals from 1990 to 2015, finding that the total number of individuals migrating has oscillated around 1% of the global population per five-year period. My estimates contain substantial return migration flows, correcting a weakness inherent to the minimum-migrants assumption in previous estimates.