The radiation model is a parameter-free model of human mobility that has been applied primarily for short-distance moves, such as commuting. When applied to migration, it underestimates the number of long-range moves, such as between different US states. Here we show that it additionally suffers from a conceptual inconsistency that can have substantial numerical effects on long-distance moves. We propose a modification of the radiation model that introduces a dependence on the angle between any two alternative potential destinations, accounting for the possibility that migrants may have preferences about the approximate direction of their move. We demonstrate that this modification mitigates the conceptual inconsistency and improves the model fit to observational migration data, without introducing any fitting parameters.