Inferring human demographic history from extant genomes is an important goal of population genetics. To date, the sensitivity of coalescence-based methods in detecting population bottlenecks has not been well characterized. In this study, we find that brief bottlenecks, of just a few generations, are undetectable by current methods. A new approach to population inference, Lineage Time Inference (LiTI), uses data-derived windows to demarcate the limits of the genetic data. We find that a sharp population bottleneck at the time of the Youngest Toba Eruption, and also at more ancient timepoints in the human lineage, would be outside the genetic streetlight.