An influential strand of research has tested for the effects of immigration on natives' wages and employment using exogenous refugee supply shocks as natural experiments. Several studies have reached conflicting conclusions about the effects of noted refugee waves such as the Mariel Boatlift in Miami and post-Soviet refugees to Israel. We show that conflicting findings on the effects of the Mariel Boatlift can be explained by a sudden change in the race composition of the Current Population Survey extracts in 1980, specific to Miami but unrelated to the Boatlift. We also show that conflicting findings on the labor-market effects of other important refugee waves can be produced by spurious correlation between the instrument and the endogenous variable introduced by applying a common divisor to both. As a whole, the evidence from refugee waves reinforces the existing consensus that the impact of immigration on average native-born workers is small, and fails to substantiate claims of large detrimental impacts on workers with less than high school.