Casualty counts are often controversial, and thorough research can only go so far in resolving such debates—there will almost always be missing data, and thus, a need to draw inferences about how comprehensively violence has been recorded. This article addresses that challenge by developing an estimation strategy based on the observation that violent events are generally distributed according to power laws, a pattern that structures expectations about what event data on armed conflict would look like if those data were complete. This technique is applied to estimate the number of Native American and US casualties in the American Indian Wars between 1776 and 1890, demonstrating how scholars can use power laws to estimate conflict size, even (and perhaps especially) where previous literature has been unable to do so.